Setup:

The game I'm running has the party engage in combat with sea monsters while out at sea.   I'm using the Sailing Ship stat block for a ship that will be involved that has a Ballista onboard which will be used during the combat.  (At least I assume.)

Question:

1) Is there anything in the Ballista text, or other RAW, that would not allow having three people manning a Ballista performing one of the three actions (See Below) on their turn to fire the weapon each round?

2) If the answer is yes, could a player Ready an action saying "When Player X loads the Ballista I will aim the device at Target Z", to which the following player Ready their action declaring "When Player Y aims the Ballista I will fire the device at Target Z"

Ballista

Large object

Armor Class: 15

Hit Points: 50

Damage Immunities: poison, psychic

A ballista is a massive crossbow that fires heavy bolts. Before it can be fired, it must be loaded and aimed. It takes one action to load the weapon, one action to aim it, and one action to fire it.

Bolt. Ranged Weapon Attack: +6 to hit, range 120/480 ft., one target. Hit: 16 (3d10) piercing damage.

I don't know what RAW is, but I would be fine with both 1 and 2 as a GM. 

Realistically unless someone has a proficiency that requires them to go in a particular order (highly unlikely), I would suggest as DM, to just roll initiative, and have the highest initiative load, 2nd highest aim, 3rd fire. I assume things like DEX do not factor into the attack. (At least, they shouldn't.)

Thanks!  That is where I was leaning but a second opinion never hurts. 

Also, the Sailing Ship (from Ghostmarsh), has the Bastilla Action block as

Ranged Weapon Attack: +6 to hit, range 120/480 ft., one target. Hit: 16 (3d10) piercing damage.

So I would think it wouldn't take into account the character Dex bonus.

Right. The thing is bolted to the deck of the ship, and the ship is rocking on the sea. Personal dex is not relevant. Especially if someone ELSE aimed it. All you're doing is pulling the "trigger."

From a game balance standpoint it seems fine, if three characters want to spend their round to make a single attack, more power to them. The more I think of it, it seems like a bad idea, and they’re probably be better off shooting their longbows or casting some long range spells. But that’s not nearly as cool and unusual as shooting a siege weapon at a kraken, so I get it. 
In practice it would seem a bit weird to have player y holding it steady while player z reaches around them to get at the trigger, and does so without knocking the aim off track might be hard. 

From a game mechanics point of view, I think what the OP asks is fine.

I don't think a trained crew could fire a ballista every six seconds, but realism isn't the number one consideration.  I think it takes a bit of time just to "wind" the ballista.  It also depends on how big the ballista really is.  There are Scorpions and ballistae, and I'm not sure if there are other designations for the arrow throwing devices.  Some of them are pretty darn big.

I see no problem with three people taking three actions in rapid succession to load, aim, and fire the ballista.

Seems fine to me. I wouldn't force the party to go through some dance in order to figure out how to work their actions. The three players would just say they're doing the ballista thing and it fires on the lowest initiative.

As long as the enemy ships can do the same things that the PC's can do it's balanced and will be fun and that's all that counts.

I'm running a campaign that's mostly ocean based and one thing that I discovered is PC's can easily clear the deck of a ship with a simple Shatter spell.  Ships require lot's of low CR sailors to run them and PC's can, and do, just mow them down the way you and I mow grass down with a lawnmower.  So you'll have to take that into account without nerfing the PC's or over powering the other ship.

If you look at the mechanics of a ballista, it would be hard to speed it up. You can’t aim until the bolt is placed. You can’t place the bolt until the ballista is cranked back. And you can’t start cranking it back until a bolt is fired. 

The crank handle is close to where the trigger is and would be impossible to crank it unless you were in the shooter position. If you had someone trying to place a bolt before the ballista was completely activated, “work place accidents are going to happen.”

18 seconds is rather fast for something like this. Fires 3.5 times a minute. Just go with the RAW. If you did want to bend the rules some, have it fire every two rounds, but with disadvantage. 

Unless your firing a harpoon, three long bows are better than one ballista. Faster and cheaper.

Or your using some variant ship damage and it can only be done by ballista or bigger weapons. Such as the hull can only be damaged by hits totaling over 30(or what ever you set it at) points at a time.

That is one of the reason the Greeks and Romans had rams at the water line on their ships instead of just archers or ballista. A strong single hit could sink a ship but a thousand arrows would never put a hole in it. Though the ram would never kill a single sailor.
They find the rams every place an ancient ship battle happened. Half the time they came off the attacking ship after a few hits.

Yeah, it's noted in the DMG that large objects/structures can be assigned a Damage Threshold, which means any damage needs to meet or exceed that threshold to be applied to the object. It's good for ships to avoid the poked full of holes bit.

Regarding the Ballista specifically, I think the concept is that it's meant to be manned by a crew of NPCs on the ship. Good way to have multiple NPC's active and contributing without having to run a bunch of extra rounds.

Quote from The_Ace_of_Rogues >>

Yeah, it's noted in the DMG that large objects/structures can be assigned a Damage Threshold, which means any damage needs to meet or exceed that threshold to be applied to the object. It's good for ships to avoid the poked full of holes bit.

The heavier Ghostmarsh ships have a damage threshold by default on their hull. It's only other parts like the sails, helm etc. that can be harmed by weaker weapons (but things like the helm may be blocked by positioning). But attacking those things only impede the target, they won't destroy it.

For example the Sailing Ship has a damage threshold of 15 for its hull, so your average longbow simply cannot hurt it without a critical hit (as a roll of an 8 with +5 DEX is only 13), though a Ranger might manage it with hunter's mark and/or other added damage.

This makes the ballista a better weapon for damaging other ships, especially for the crew who are unlikely to be heavily armed themselves.

I ran a nautical adventure recently, but I discouraged the players from manning the weapons (cannons in this case) themselves since that's what the crew are trained to do, but instead I let players train with the crew so they could help and oversee them in action if they wanted, letting them roll to see how helpful they are, then they rolled for the crew with a bonus based on that (or penalty if they'd rolled poorly but none of them did).

RAW, Ballista's have their own stat blocks like ships. Stat blocks assume one action per turn unless otherwise specified. Ship stat blocks explicitly say that they can take multiple actions on a turn, depending on whether they are fully crewed or not. Ballistae stat blocks say nothing, so it is understood to have one action per turn. It is the Ballista's action and not the player's that is used to load on one turn, aim on the next, and finally fire on the third turn.  It requires 3 crew to man a ballista just to get the one shot per three turns. 

This one shot per three turns is why Spelljammer: Adventures in Space says :

"A spelljamming ship typically has one or more shipboard weapons, ballistae and mangonels being the most common. Such weapons are slow to load and fire. Player characters are almost always better off using their own weapons and spells in ship-to-ship combat, reserving shipboard weapons for targets that are too far away to be damaged by other means."

[ Spelljammer: Adventures in Space --> Astral Adventuring --> Ship to Ship Combat --> Ship board Weapons. (Sorry I don't know the page, I own the digital copy) ]