So, after an encounter with a suit of Animated Armor one of my players wants to create his own. Yet looking around I cannot find how they are created. How would you go about doing this? I was thinking about reflavoring the "Create Magen" spell from Rime of the Frostmaiden but that would mean he wouldn't get it till nearly the end of the campaign and thats unappealing. So what would you do?

If they wanted to do something similar temporarily I would suggest Animate Objects.

For a more permanent version, either a Battle Smith’s [Tooltip Not Found], or as a Rare (or rarer) magic item.

He's looking for something permanent. I think I'm gonna have it basically act as crafting a magic item combined with Animate Objects. I might split the difference between crafting a rare and an uncommon item. A three weeks or a month of crafting time with the party blacksmith helping and 1k gp. If they are using an already enchanted set of armor I'd reduce the costs to like 200gp and maybe two weeks crafting time.

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If you don't want to read through all 25 uses on that link, in short, use Bestow Curse:

#21: Animating Curse: Using the curse in this way raises the casting time to 10 minutes and it is cast as a ritual and does not use a spell slot but requires 300gp of additional ritual components such as herbs, incense, blood and engraved bones which are consumed by the spell. The caster places a curse to create one of the following effects & creatures created via this curse remain animated until they are destroyed or subjected to a remove curse or dispel magic spell.

1. Animated Armour: If the curse is cast on a suit of armour in a site where some one has died the caster can bind a splinter of a soul from one of the fallen into the armour and animate it as per the Animated Armour construct (see the Monster Manual). It takes the casters bonus action to command the animated armour. The armour must be mundane and you cannot animate magical armour.
2. Flying Weapon: If the curse is cast on a weapon in a site where some one has died the caster can bind a splinter of a soul from one of the fallen into the weapon and animate it as per the Flying Sword construct (see the Monster Manual). It takes the casters bonus action to command the Flying Weapon. The weapon must be a normal mundane weapon and you cannot animate magical weapons. If you hold onto the weapon and try to fly with it then you need to succeed on Strength check to maintain your grasp and the weapons speed is reduced by 50%.
3. Cursed Rug: If the curse is cast on a rug in a site where some one has died the caster can bind a splinter of a soul from one of the fallen into the rug and animate it as per the Rug of Smothering construct (see the Monster Manual). It takes the casters bonus action to command the Rug of Smothering. The rug must be mundane and you cannot animate a magical rug. The Rug you are cursing must also be worth at least 100gp.
4. Animated Scarecrow: If the curse is cast on a mundane scarecrow in a site where some one has died the caster can bind a splinter of a soul from one of the fallen into the scarecrow and animate it as per the Scarecrow construct (see the Monster Manual). It takes the casters bonus action to command the Scarecrow.
5. Animate Cursed Stone: If the curse is cast on someone who has been petrified, the caster can bind a splinter of the petrified soul and animate the petrified statue as per the Stone Cursed construct (see Mordenkainens Tome of Foes). It takes the casters bonus action to command the Stone Cursed

A variant of Create Undead is basically what you're looking for. [Permanent creation of a CR 1 monster]

It may require some rebalancing, since there are a lot of well-known resources for dealing with undead specifically, but that would be the place to start. Other attempts at construct animation spells tend to be deliberately non-permanent for whatever reason. Tiny Servant is a good example.

I suspect the reason that Constructs aren't designed to be permanently animated is that failing to control undead carries a lot of risk, whereas losing control of a construct would probably just result in it standing in place and growing dust, or just wandering off in a random direction. Undead also register as evil, so it can lead to problems in non-evil campaigns, whereas Constructs won't necessarily raise any flags.

The other option is to look into the Shield Guardian and Master's Amulet. That's a Rare item with crafting rules and a CR7 monster. No specific rules for creating a Shield Guardian, but maybe they could craft an amulet that would basically animate a suit of armor under the same principles. That would also prevent them from creating an army.

Maybe require a magic item like a Manual of Golems the gold and time requirements scaled down? 

i would look into what others posted specifically thr masters amulet and thr golem manuals.

Careful with the golem manuals because even the cheapest one, RAW is insanely expensive & time consuming.

I also wouldn't be so worried about the level suggestions (rare+ should be given at like level 9+). Or more accurately I would but would start a multi step quest of some sort that take it, it not at that level than close to it or even past it.

The fact that it's not a RAW thing is a reason. That it's not in any PC class feature also means it's not 'normal' for a pc to be able to this.. But dnd is all about homebrewing so lets go ahead.

Let them find a broken or not working masters amulet. Either found in a ruined lab or gifted by a wizard (or someone who can get their hands on old wizard stuff). Work on some quests to repair it. They need to find a knowledgeable wizard who knows what's missing then another quest to get the components then another to actually find a blacksmith. Then when they have it they still need to construct it.

Or do the quest in reverse. Let him find an old peice of cursed armor but now he has to look for an amulet to control it. Etc