A Center Controller reported an air carrier crossing into Mexican airspace experiencing a pressurization problem was descended to an altitude approved by the Mexican ATC facility but was below the terrain requirements of the Center Controllers.

Narrative

Busy weather day with complex traffic and frequency congestion. Palomas WEDCA was active FL280 and above until XA:00. Aircraft Y was in the middle of the WEDCA when he said he needed 100 MSL for a pressurization issue. I immediately gave him FL290 until we could coordinate with MTY. My D side called MTY and said 100 was approved and that they would let CJS approach know. I told my D side to call ELP approach as well to let them know and to have them coordinate with CJS as well because we don't have a direct line. At that point Aircraft Y was asking for lower as the situation was becoming imminent. I gave the Aircraft Y 100 and told him to squawk the code of XXXX as he was entering MTY and CJS controlled airspace and they had no idea where he actually was. I checked the terrain map but we don't depict Mexican terrain on our maps. After checking that area later on a website; the highest peak is about 8600ft which would've busted our 2000ft above the highest obstacle requirement. ASH eventually diverted to ELP and safely landed on the ground.1. We need to be able to depict Mexican terrain on our maps if we're going to be continuing to work aircraft in Mexican airspace.2. We need a direct line to CJS approach. There have been countless times we need to coordinate with CJS especially during weather season. Instead; we have to go through MTY or ELP and you never quite know what's being coordinated. 3. We're relying too heavily on the Palomas WEDCA working out and need to route more aircraft away from the ELP area during weather events.