Are there any requirements for transporting the rifle or ammo in the car?  For example, to the range or a range in NY.

Thanks.

Check packing.org, they should have Interstate Transport laws listed there.  Just to be safe, what I alwasy do is have rifle in trunk, locked in case with some sort of locking device on the weapon itself, and ammo in another part of car, usually the passenger seat.  That seems to be what most states ask for, and it seems pretty reasonable if you were to get stopped and questioned.  Hope this helps.
edited to add:  you could also check the NRA website, I know they have interstate transport laws there too.