Thanks for all the suggestions so far!
I just thought I’d mention that I’m running a pretty basic “beer and pretzels” style game, and the players seem to want basic magic items with numerical bonuses over fancier stuff.
I prefer the latter myself and would rather not include +x items if I can help it, but they specifically asked for a +2 battleaxe for the barbarian.
The problem with +X items is that they are far more effective than they look.
This means power creep; a character with a +2 axe is going to change the CR of foes the character can defeat by a non-zero amount. And it isn't all that cool. Plus, +X items are fungible; you can swap one for another.
In short, don't give them what they want. Bwahaha. Give them instead something awesome!
Here, what I'd give them is an axe that deals 3d6 damage, +1d4 lightning. You might say "wow, that is an amazing axe", but
it isn't as good as a +2 axe.
Suppose you have a level 10 barbarian with 20 strength attacking an AC 20 target recklessly, with -5/+10 from GWM. +4 to hit for 21.5 damage.
They hit 44% of the time and crit 10% of the time doing 10.11 damage per swing.
Give them a +2 Axe. They now hit for 23.5 and hit 58% of the time and crit 10% of the time for 14.28 damage per swing.
Now, give them the above axe; it does 28 per swing, hits 44% of the time and crits 10% of the time. It does 13.62 damage per swing.
Less than the +2 axe. This is key; we made a crazy axe that isn't as good as a "boring" +2 item.
We can now add on fun stuff without overpowering it.
1. It requires attunement, but not for the one who got it blessed at the altar.
2. It is a 30/60 range throwing weapon. Throwing it while in melee range does not cause disadvantage.
3. It returns to your hand at the start of your turn if you will it, moving up to 200', so long a there is a path. (If more than 200', it will start returning)
4. On a critical hit, you can unleash a thunderclap that can be heard from 100s of feet away: if you do so, all creatures of your choice within 10' must make a strength save (DC based on wielders strength: 8+prof+strength) or take 1d12+strength thunder damage, be knocked prone, and pushed 20' away.
I like the treant wood handle. Combat? Diplomacy? Either works. And then the weapon has to be blessed at the altar of god of thunder on top of the mountain. The wielder must stand on the altar, and be struck by lighting through the weapon. If they are judged worthy, the runes will activate.
Part of the deal here is that this weapon isn't fungible. You find another cool axe? Is it better or worse? It will be different.
Also, a neat item like this begs to be upgraded. Make a plan to upgrade that lighting damage to d8 (I made it d4 so it looks different than the d6s; so you can roll 3d6 and 1d4 at once; so skip over 1d6) at some point, in a tier or so, and throw on something else (maybe you can throw it in a line, attacking each foe granting cover to a target in order, or everyone along the line has to make a dex save).
This "stormbringer" axe is (in most situations)
weaker than the +2 axe the PCs are asking for. Now, which axe will PCs remember and think is cooler?
Even in a beer and prezils game.
...
What more, that +2 item, as accuracy piles up the DM ends up wanting to boost enemy AC; but this in turn makes characters without +X items become more gimped.
They also want things like a +1 breastplate, a cloak of protection, a luckstone, etc. All the things that provide numerical bonuses!
Yes, again, +X items are crazy strong and don't feel strong.
Also, many don't require attunement. So you can stack them on top of a PC and keep getting stronger, unlike attunement items.
Are you sure they want +X, or maybe they find +X easier to convince you to give them?
Would they wear a cloak of protection over a cloak of displacement? I suspect the second. But the first is easier to convince a DM to give you.
The wizard already had an arcane grimoire +1 and has just bought a wand of the war mage +1 (for an effective +2 on spell attacks).
At first I was panicking a bit but then I reminded myself that this is just a beer and pretzels game. Let them have their +s if that’s what they want.
Also, one of the PCs is a forge cleric, so can make a weapon or suit of armor a +1 through his class features. Kind of hard to ban +x items when one of the PCs has it as a built-in class feature!
Sure, the Forge cleric can make
one +1 item. By avoiding +1 items elsewhere, you also avoid that feature becoming obsolete!
A PC should always need a item converted to +1 by the forge cleric. Ideally more than 1, so there is choice.

<- evil
I might also suggest using random magic item tables to determine what is for sale in an area, rather than some kind of universal price list. And use the price ranges in the DMG for how much they cost (as items aren't easily available, the fact that worse items cost more than better items doesn't fundamentally matter; they can choose to buy an item at the price asked, or not. They won't be able to sell the item for the price they bought it either, unless they run into someone who wants that specific item.)
---
Adamantine armor that grants 10 temporary HP at the start of your turn.
Cloak of Displacement
Cloak of Invisibility
Ring of Invisibility
Stone of Fortune (At midnight, roll 2d20; you can swap any ability check or saving throw you make with these dice).