Is anyone else having an issue with equipping this? It doesn't change my AC like other items do.

This item would not change your AC unless you are playing a barbarian with there "Unarmored Defense" class feature. This would increase your HP of any character but it does require attunement which once equipped there will be an additional button for that. There is also a 3 attuned item limit.

Cost?

See the PDF "Sane Magical Prices". Google it you'll find it!

Guess there is none, I’m using 5 gold 

http://anyflip.com/jcns/whcb/basic

My rogue is wearing one of these, and should have hp's of 39 (he is 4th level), however Beyond is capping this at 34.

Any ideas of a fix?

Quote from DaveBlewer >>

My rogue is wearing one of these, and should have hp's of 39 (he is 4th level), however Beyond is capping this at 34.

Any ideas of a fix?

 

Sometimes things seem to be bugged when editing a character, more so say items. Try completely removing the amulet from the inventory, re-add it and then equip/attune it. See if that fixes it.

As always, it was my own stupidity. Worked out what I did wrong. :)

While attuned to this item, does it change your base constitution score to 19, not counting racial bonuses, feat bonuses, or other magic item bonuses, or just increase your total, to 19 no matter what bonuses you have?

It sets your score to 19, regardless of other modifiers.

Quote from BruhMomentvibecheck >>

While attuned to this item, does it change your base constitution score to 19, not counting racial bonuses, feat bonuses, or other magic item bonuses, or just increase your total, to 19 no matter what bonuses you have?

 It changes your constitution score (negating all modifiers) to 19, unless it’s otherwise higher.

So why 19? There is absolutely no difference between 18 and 19, correct? And you can never add +1 con to get to 20 with the item.

@Mattakar Honestly, I think to frustrate you and make you consider getting a different item and maxing the score someday haha.

Seems good for a Blood Hunter, considering the amount of HP they could use

When using this item on the D & D beyond character sheet, it not only increases your constitution in the associated bonus but also your hit points and hit point maximum.  I wonder if I wonder if that what was intended?

That is by design.  Each time you level up, your HP increases by your hit die (whether you roll it or take the average) plus your Constitution modifier.  When you increase your Constitution modifier by 1, your max HP will also increase by 1 for each level your PC has gained.  For example, if your PC turns level 8 and uses their ability score increase to increase their Con mod by 1, they will immediately gain 8 additional max HP. 

The Amulet of Health should increase a PC's max HP by in the same way.

My battle smith artificer made this one of his infusions as soon as he got to level 14, and he had a -1 Con modifier.  He went from 59 hit points to 129 immediately.  I also got the Durable Feat 2 levels earlier because I knew exactly what having this meant.  

Not only did he "seem to look much more healthier" as my DM put it, but now whenever he takes a short rest, he automatically gets back 12 hit points for each die I use.  He's the party healer too, so he can save his spell slots for the rest of the team and if he ever loses the item, he can just tie a coin to a string and infuse that.  This item is a must-have for characters that want items like Gauntlets of Ogre Power and want to take the risk of dump-stating.  Xanathar's Guide says it would take 10 workweeks and 2,000 gold to craft.  If you're willing to make the investment, you can have it much earlier and sell it once you learn the infusion.

Quote from The_RJ >>

My battle smith artificer made this one of his infusions as soon as he got to level 14, and he had a -1 Con modifier.  He went from 59 hit points to 129 immediately.  I also got the Durable Feat 2 levels earlier because I knew exactly what having this meant.  

Not only did he "seem to look much more healthier" as my DM put it, but now whenever he takes a short rest, he automatically gets back 12 hit points for each die I use.  He's the party healer too, so he can save his spell slots for the rest of the team and if he ever loses the item, he can just tie a coin to a string and infuse that.  This item is a must-have for characters that want items like Gauntlets of Ogre Power and want to take the risk of dump-stating.  Xanathar's Guide says it would take 10 workweeks and 2,000 gold to craft.  If you're willing to make the investment, you can have it much earlier and sell it once you learn the infusion.

 Or reverse, Infuse one then free that infusion later once you've crafted!

@Mattakar I’m guessing that since there are/could be effects that reduce stats, better to have the highest point value.