NCT Controller described an attempt to hand off an IFR aircraft to MRY that was denied entry by the Tower. The Controller suggested that TRACON controllers receive training on this eventuality.

Narrative

A C310 was handed off to me from the adjacent Morgan Sector; IFR; level 7;000 FT; on V111 toward SNS; cleared to MRY; with an inoperative transponder and non-DME equipped. MRY airport was advertising LOC/DME approach Runway 28L. C310 requested the ILS [Runway] 10R approach into MRY. I coordinated with MRY Tower when said aircraft was approximately 25 miles north of the airport and the operation was approved by the Tower. As [the] C310 got closer to the airport; MRY Tower called back advising me that the C310 was unable to land at MRY with inoperative transponder. I then notified the Supervisor of the information I received from Tower; then called MRY back to confirm that they knew the C310 was IFR; inbound to MRY. They advised that unless he was based out of MRY or the transponder failed in flight that he was unable to land at MRY. As I was coordinating with the C310 the situation with MRY Tower; the C310 requested a clearance to a different airport in my airspace. At that point I issued a new clearance to the C310 to WVI airport and pointed the C310 out to MRY Tower. Recommendation; training [is needed] on how MRY Tower would like NCT to handle non-transponder aircraft inbound to MRY.