Cozies- Absorbent layer or no?

I dont see the harm but only if the cozy is for holding the pig an ones lap otherwise just regular ones should be good in the cage.

Now sure how you could add absorbant stuff but you may be able to replace the batting on the bottom with a cutout from a baby pad changing water proof blanket thingy im not sure maybie microfiber towel a few lauers instead of batting lol lets see what happens

I use a few layers of batting, that seems to work great
For lap pads, sew in a table cloth or shower curtain. You'll never get peed on again.