Two light aircraft experienced what was described as a NMAC following a failure by the reporter to report a fix prior to circling for landing following a practice GPS approach to RNM.

Narrative

My student and I were operating under an IFR flight plan on a training flight in his aircraft into Ramona; CA (RNM). As the Instructor and more experienced pilot; I was acting as pilot in command and; as the pilot not flying; was communicating on the radios as my student flew the aircraft. After receiving our approach clearance for the GPS Runway 9 approach into RNM from SOCAL Approach; we began our final descent along the approach course of 085 degrees. We had listened to the RNM ATIS; which was reporting a ceiling of 1;300 FT and Runway 27 in use; accordingly; we expected a circle-to-land to the south (as circling was not authorized north of Runway 9/27) into the left downwind for Runway 27. After confirming that we were established inbound; SOCAL Approach switched us over to RNM Tower; and I reported that we were 'Inbound on the GPS 9 approach; circle-to-land to Runway 27.' Tower instructed us to 'Circle south; left downwind for Runway 27 at AYODA' fix; which I confirmed in my response. We continued our descent to our circling MDA of 850 FT AGL; and finally broke out into VMC about 1 NM past AYODA. With the airport in sight; we began our right turn into the left downwind for Runway 27 at 2;300 FT MSL. As we maneuvered; another pilot in a Citabria radioed in to Tower that 'aircraft X just missed us. They're right above us now.' To confirm our position for both Tower and the other aircraft; I reported that we 'were now on left downwind for Runway 27.