B737NG experiences descend TCAS RA on climb out from RNO. Resolution maneuver results in GPWS terrain warning due to rising terrain.

Narrative

Upon departure from RNO (heavy: 143;000 LBS); received notice of a Bonanza at 6;000 FT (1;500 FT AGL). At the same time; TCAS presented a target in front of us with a +200 FT separation. The target was immediately yellow; and then an RA instructed us to descend. The Captain immediately descended as the flaps were still retracting. The TCAS commanded a 1;500 FPM descent. We were 1;500 FT AGL at this time. While complying with the RA; the aircraft Ground Proximity Warning System issued a caution; 'Don't Sink; Don't Sink.' The Captain immediately arrested the descent and then commenced a climb. We never saw the traffic. We were only 1000 FT AGL and the terrain was rising in front of us (red on the EFIS screen). The aircraft was able to climb safely away from the terrain once the climb was commenced. The Captain called the Tower the next day and related to me that the Bonanza was on a downwind and the Tower thought there was adequate separation. Our B737 apparently thought differently; resulting in something that should be of concern; an RA commanding a descent at a low altitude in rising terrain in Reno. I have never had a Resolution Alert at such a low altitude; and I have never had a ground proximity caution resulting from a TCAS RA maneuver. We could not out climb the Bonanza; it was directly in our climb path. Even if we saw it; which we didn't; we were in a canyon without room to maneuver clear; other than descending and passing underneath it at 1;000 FT AGL. The RNO Tower should be made aware that VFR separation from GA may not be adequate for departing Part 121 aircraft. Because of the terrain; Tower is probably used to very close-in patterns by VFR aircraft; which conflicts with the TCAS 'bubble' on our aircraft. Descending into rising terrain in Reno is a no-win situation; we were lucky it was daylight.