A television service didn't reach BELIZE (aka British Honduras) until 1981 - Tropical Vision, on channel 9.
Although Doctor Who was not shown on the local terrestrial TV station, viewers who could speak Spanish may have been able to tune into transmissions from Mexico and Guatemala during the early 1980s (or in the late 1970s if they already possessed a set to view cross-border TV prior to 1981).
By 1980, a limited television service had also been established by the British Forces Broadcasting Service (BFBS), which supplied a weekly dispatch of video-taped programmes to the British military bases in Belize. These may have included the final Tom Baker season, and all the Peter Davison, Colin Baker and Sylvester McCoy series.
It's possible that satellite stations such as the Spanish-only HBO OLE were also available in the 1990s.
As an aside, during the visit to the Altun Ha pyramid in Belize as part of the "Sci-Fi Sea Cruise" in December 2003, Terrance Dicks was recognised by one of the guides and asked to sign autographs; presumably the guide had seen the series via one of these providers!
- PHOTOS from that trip can be seen here
- Video footage taken in Belize and 'interview' with Dicks is here: