I noticed Fastenal was listed for stainless. They have some that's for sure, but since they went no cash allowed and accounts only I haven't been in there. I do check their website for things from time to time, but anything i need right now is never in my local store. I found atleast over the counter Copper State Bolt has a better selection of stainless, lower price, will take walk-in cash customers (maybe not during covid), and will sell smaller quantities. They are not nation wide to my knowledge. Just a western states chain , but they are expanding. Their prices are good enough on the small stuff I usually just buy 100ct box even if I just need a hand full. https://www.copperstate.com/
McMaster was already mentioned, but they are a great source for stainless as well. Huge inventory and selection. Better selection even than Copper State. They tend to be a little more than Copperstate, but always less (when I check) than Fastenal. McMaster has a reputation for being expensive in the industry, but when I actually check on many things they are quite competitive, and they ship very fast.
MSC is am industrial supplier who also has some stainless. Sadly they are geared towards commercial customers. Their catalog price and web price is usually on the high side for everything. I didn't do business with them for years because of it. When they bought Enco and proudly announced I was now one of their customers I wasn't to happy. I told them so. That I would not buy from them at catalog prices or their published web prices. They told me to logon and check my business prices since my Enco business account was now in their system. They are pretty competitive, but unless you setup an account and logon to their website you will never see those prices. They do run discounts and shipping code specials almost everyday, but my business price is usually lower. Don't know how that would reflect with a new customer.
I get most of my rivets from Bolt Depot or McMaster. Stainless or aluminum.