Many of the infused Items don't exist as normal items with a rarity we can calculate to make permanent versions. 

Me specifically, I want to make a returning Boomerang form my Drunken Fist Monk, give her a ranged attack option.  But this goes for anything that's outside of a simple +1 or Replicate Magic Item.

Most of these items are uncommon, but I don't know if that's a good baseline.

So update, i finally realized that a ranged weapons are not monk weapons, but the question is still a good one.

uncommon seems pretty fair for most of them, maybe a few would tip into rare, and others might belong at common

My current artificer is researching Returning Daggers using his own Magical Infusion such item as a template for a permanent version. I have completed the downtime for the research portion of the work. Now I just need the Downtime, in one chunk, to do the crafting and see if I am successful.

If your DM allows it, you could use the alternate method for determining monk weapons outlined in this Class Feature Variants UA:  https://media.wizards.com/2019/dnd/downloads/UA-ClassFeatures.pdf

Quote from hebeach89 >>

uncommon seems pretty fair for most of them, maybe a few would tip into rare, and others might belong at common

 I agree with hebeach89.

Uncommon is a good rarity for Returning Weapons, it fits the normal pattern for uncommon weapons, a +1, and minor benefit.

[Tooltip Not Found] apparently already exists, but there seems to be no page for it for some reason. I found that out when I made a returning dagger and it wouldn’t let me publish because it was too similar.

Well, update on the boomerang front.  My DM stated that it made no sense that there were no ranged Monk weapons.  Our monk will still prefer to be up close and personal, but I wanted to give her a ranged option, and the DM said he will consider darts and Boomerangs as monk weapons.

I'll see what the DM says if she shows an interest in keeping the infusion on that boomerang.

Daggers, Handaxes, Light Hammers, and Spears are all monk weapons and have the same thrown range as Darts. The Javelin is also a Monk Weapon and has an even better range.

Infused items are further complicated by the fact that some of them have a DC for their effects (Radiant weapon, Repulsion shield, etc.), and Wizards took the cheap route of saying "your artificer spell save DC" when constructing them.  This means that when constructing permanent versions thereof, you need to assign a fixed DC, and in many cases your artificer DC is going to be significantly higher than most magical items allow their DCs to be.

This came up when someone in my party located a Radiant battleaxe as loot, and I had to jigger the weapon to work in the builder despite DDB very, very seriously not wanting it to.  It's an issue even for simply sharing your infusions the way everyone insists an artificer should; if you can't put "Radiant battleaxe" on your allied party member's sheet without janky homebrew, it's gonna be real hard for them to use this thing you're trying to let them have.

I started to laugh when you said returning boomerang. But then I realized you must mean one that actually hit something.

I carry 4 so it's not a problem. Through group jokes my character morphed into a Batman analog named Pantherman.