I have had very good luck with the Brownells Alumahyde coatings. Much more durable than the standard Rustoleum & Krylon aerosol cans, and it holds up very well to cleaning chemicals & moderate heat. You can bake it for a few hours to cure, or let it air dry for 10-14 days, so it allows flexibility if you don't have access to an oven.
The temperature resistance you need will depend on how you plan on using this barrel. If you're doing a lot of rapid fire drills, the high-temp BBQ spray or automotive coatings will hold up well. But if you're planning on using this for rapid fire use, then maybe a chrome lined barrel might be a better option since it's more durable at the high temperatures from sustained rapid fire. If it's going to be used to fire in short strings for precision target shooting, with an occasional burst, then any standard paint should be just fine.
Either way, I'd definitely tape off the gas block journal from coating, or simply coat the barrel with the gas block in place so that coating buildup doesn't interfere with the fitment. Even a light coating (0.001" to 0.003") could cause interference to the gas block fit, or could cause the gas block to scratch the coating as you slide into place. This happened on one of my heavy-profile barrels -- which wasn't the end of the world -- but I had some extra touch up to do afterwards.