In addition to the sanctioned CMP games matches (Springfield, vintage bolt, John C Garand), many clubs hold vintage shoots following the same basic rules or a modified course, often scaled to 100 yard targets. They are a fun course to shoot, and even with a basic Mosin Nagant with a decent zero, decent surplus ammo or "wolf", a couple of stripper clips and an M1 Web sling you can do fairly well. If you happen to have a good shooting M1917, M1903, K-31, Swedish M96 or M1 Garand with quality ammo and know how to use it, you can be competitive at Perry and you can start collecting expensive pins for your hat.
Another really fun CMP event that is not widely held, is the Vintage sniper match. Fired at 300 and 600 yards with a WWII or repro sniper rifle. The top shooters invariably fire an M1903 or Swedish M41 variant $$$, but you can do well enough to have fun and scare them a bit on a good day with a Mosin Nagant PU resto/repro and quality ammo. It is shot in 2 man teams on targets that are shown only for a short time. In that time, your previous shot is spotted, correction if any is made, you aim and fire. Very fast paced, and especially interesting on a windy day. I was killing it with my mosin one day, and the guy who ended up winning was spotting on a neighboring firing point. He was visibly perturbed every time my target came up 10 or 10x, and very happy 6 shots into the 600 yard stage when something came loose and my zero crossed the singularity.