I've tried small filterless tanks for bettas and IMO it's best to do small (10%-ish) water changes daily. Some people change 100% of the water weekly, but I can't help but think that's stressful for the fish as ammonia will build up all week long plus a 100% WC may cause damaging swings in temp and pH.
You perhaps already know this, but I'll mention it for others who may not: Bettas can survive in unfiltered tanks because they can gulp air at the surface, so the lack of water flow/oxygenation won't kill them -- but ammonia in the water will burn their gills and do other damage just the same as with non-labyrinth fish. Bettas really do best in filtered, cycled tanks. And, being tropicals, they do need a heater. For a tank that size, a 25w heater (or smaller if you can find one) willl do nicely.
You perhaps already know this, but I'll mention it for others who may not: Bettas can survive in unfiltered tanks because they can gulp air at the surface, so the lack of water flow/oxygenation won't kill them -- but ammonia in the water will burn their gills and do other damage just the same as with non-labyrinth fish. Bettas really do best in filtered, cycled tanks. And, being tropicals, they do need a heater. For a tank that size, a 25w heater (or smaller if you can find one) willl do nicely.