Pushes are always a chest exercise, pulldowns and pullups are a back (lat) exercise. They aren't interchangeable in terms of body parts affected.
Try doing lying dumbbell pullovers or barbell pullovers with straight arms. I think we had a thread about this a few weeks ago...let me see if I can find the links.
Here's how to do a barbell pullover:
http://www.exrx.net/WeightExercises/...BPullover.html
Lie with your shoulders supported on a bench and your head just slightly off the side of the bench. Extend the barbell back over your head with straight arms, them back up again.
If you bend your arms, it becomes a tricep exercise.
Another alternative is resistance bands. You can get them fairly cheaply (at least here, and loop or tie it to a high piece of furniture. Do seated high pulls.
Mel