I searched a few websites. There is a one stop that goes SDQ to JFK and JFK to GUA. Since I did not have an exact date, I chose one-way on Aug. 16, 2006 as a benchline date. That flight involved AA and Taca. It was around 440 dollars.
Copa also is possible. The flight is SDQ to Panama and Panama to GUA. One way for that was more, slightly over 500 dollars.
Edited to add:
I know you said not AA - but thought I'd mention it since it appears to be a les expensive option.