I have court ordered community service in queens, NY. Unfortunately I need to move to richmond, virginia ASAP. I need to know if the service can possibly be transferred.

First you are not going to be able to just move if community service is part of probation. You would have to ask for it to be transferred.

I know in Atlanta, they had an approved list of where you had to do community service,

So are you on probation to complete it ?

First you are not going to be able to just move if community service is part of probation. You would have to ask for it to be transfered.
...
If you are on probation, you will probably need permission to move, period.