It depends on how close you wish the rhyme to be.
Words that ony change the first letter include tapers, rapers, capers, and vapours (although it's spelt differently, it's often pronounced more like vapers). Other words that still rhyme, but are less obvious include rippers, slippers, dippers, clippers, etc.
No. Please see the related questions below for "What rhymes with sharper?" and "What rhymes with paper?"
Newspaper
Small paper.
Some words that rhyme with vapor are paper, caper, and taper.
Caper, paper, newspaper, vapor
Tapir rhymes with paper. Please see the related link below.
Glue.
It is glue.
sky-scraper/my-hater/five-waiters/by-haters/my-favors/
A drop of liquid from the eye (rhymes with beer), or to rip something like cloth or paper (rhymes with hair).
paper, uh... can't think of any more .. ~Caper.
Clean Caper Mean Draper Scene Taper