Suppressors suppressor pouch

By the title of your thread I'm guessing you are looking for a suppressor pouch similar to the ones that come with Surefire cans. Ray, user name "Softcock" makes some nice ones, variable length. You can find him in the "Accessories" forum.
 
I have a couple that came with AAC cans, those were actually really nice and use a molle strap. I have others that came with 'em but a sock would work as well if not better IMO. Anyway, one of those AAC covers is on a vest I never use (and hope to never have to). Just in case I guess.

Otherwise they sit on the shelf. Or on the rifle but typically not stored that way because storing the can long term on the barrel can make rusting easier given the conditions.

I have several that came with cans I'll never use. Some fit a regular belt, most are black. The cans are usually made of rust resistant material and the wear and tear just makes 'em look "serious" for lack of a better term. The only use for a pouch would be if in the field for a while and you need somewhere to store it that way. In which case it'd go in a ruck because if it fell out of a pouch you'd never know unless it was tied down. And in a ruck a sock would work just fine and be one less thing to carry.

Those little nylon cinch bags are also used. I have several (seems like they ALL used to come with one, some pretty nice) and never used 'em though, would never spend money on one.