Parrots will not spawn unless they were pre-generated with the world, once dead or tamed no new one will spawn.

Create a Superflat world with the following preset

3;minecraft:bedrock,45*minecraft:dirt,minecraft:grass;21

Kill all other currently existing entities

/kill @e[type=!player]

Wait some time
You will get ocelots spawning but no parrots
You can repeat with [code]3;minecraft:bedrock,45*minecraft:dirt,minecraft:grass;21;decoration[/code
It is the same result.

If you create a normal world and then use something like mcedit to remove all blocks then just put grass down in the jungle only ocelots spawn. Putting grass can be done manually or with fill command or making structure block for it.

For all above i recommend changing gamerules for daylightcycle and weather such you only dealing with ocelots and parrots you can also setup a counter system with the command blocks