Enumerate all solutions of a SAT problem
You are looking for an ALL-SAT or all solutions SAT solver. This is a different problem from #SAT. You do not have to enumerate all solutions to count them. 

I do not know of a tool that solves your problem because people add these algorithms on top of existing SAT solvers but rarely seem to release these extensions. Two papers that should help you in modifying a CDCL solver to implement ALL-SAT are below.

Memory Efficient All-Solutions SAT solver and its Application to Reachability, O. Grumberg, A. Schuster, A. Yadgar, FMCAD 2004

Here is a recent article posted on the arXiv.

Extending Modern SAT Solvers for Enumerating All Models, Said Jabbour, Lakhdar Sais, Yakoub Salhi, 2013

You could try contacting these authors for their implementation.