Can't be a dungeon spawner because those no longer produce villager zombies.
Yes, that changed in 1.11 when they got their own entity ID, but there's so much we don't know, like what version of Minecraft the OP is running, or whether he used a zombie villager spawn egg on a spawner in Creative and went back to Survival. I wasn't sure what he meant initially either (and I'm very much still not, TBH). But he said "spawner" and mentioned having more than 6 "villagers" would stop others from spawning (spawners have a limit of 5 mobs in the 9x9x9, but with mob grinders you're only limited by the much different dimenson mob cap of (typically) 70 in singleplayer).
But I know what you mean. Maybe I read too much into a short post and he is talking about some kind of grinder setup, though. That was actually my first thought, then I changed my mind. OP, we need you. :-)
More information, please. Are you talking about a mob spawner block (cage with a mob inside of it that spawns that mob when you are nearby, such as those generated in mineshafts and dungeons)? It sort of sounds like that's what you're talking about. If that's the case, the key to getting good rates is to move (and keep) the mobs 10+ blocks away from the spawner as quickly as you can after they spawn. The longer they linger in the 9x9x9 cube, the more spawning chances you miss.
There are a lot of ways to do that. If your spawner is high enough, you can drop them into water 10+ blocks below, and funnel them to a collection area with water streams. Otherwise just funnel them with water streams straight away; it'll be a bit slower but you have at least 10 seconds before the next pack spawns anyway. There are other fun and creative means, like baiting zombies with a trapped (but safe) villager, piston pushers, flying machines, and many more. But if you just want good rates, it's usually hard to beat good old flowing water.