Writing rivetter with a double T is accepted as a variant by Wiktionary and the Shorter Oxford. The OED dates that spelling to the 1700s and 1800s, but it is used today by some people interested in inserting rivets. For example, the Bikermart motor cycle accessories outfit in the UK offers several models of BikeIt Heavyweight Motorcycle Chain Breaker, Cutter and Rivetter Kit.
I'll add it as a rare word.
Whether it is "just as valid" as riveter probably depends on whether we regard the validity of a word as an absolute characteristic, like a driver's licence, or a matter of degree, like an argument in a debate. Discuss.
