They used to make a rimfire belt. I had one when I was a kid around 1980. My father got it for me, had to modify it as I was too small in the waist. Held like 50 rounds. That and a Stevens 22 Single Shot was a lot of fun walking around. That was as good as anything. It was canvas with a leather strip at the bottom as a stop. I'm sure it was from a gun show, K-mart (they once sold guns, most of us remember), or the local gun dealer.
Later, I used to wear a jacket knocking about in the woods, and carried a box in the jacket pocket, but that was with a Ruger 10/22 and I had magazines for it also. I tried belt pouches, but they seem to spill bullets if you sit down sometimes (at least the cheapies do).