The dominican government entity that deals with HIV is DIGECITSS (Direccion General de Control de Infecciones de Transmision Sexua y SIDA). From what I understand, the problem is not availibilty of medication but adherence. I doubt DIGECITSS would take a donation but they might be able to direct you to some NGOs/missions that provide meds and might need it.
At the very least, DIGECITSS can provide a list of the gov't UAI (unidad de antencion primaria) that do the HIV/AIDS treatment and care. In general, the clinics are very well funded thanks to the CLinton FOundation.