According to the Economy Secretariat in Mexico:
In accordance to Article 61, fraction XVII and last paragraph of the Mexican Customs Act, in sections 2.9.7 and 2.9.8 of the General Rules on Foreign Trade for 2002, the Mexican Economy Secretariat will exempt the requirement of permission imports to vehicles donated to the Federal Treasury if the purpose they are destined is [to be located at] the Federal District, states, municipalities or non-profit organizations, provided they are vehicles used solely for the attention of basic living requirements. This benefit is limited to five vehicles per year by each donor and will establish a maximum age for the unit up to fifteen years (Article 7 published on the Official Gazette of the Federation on May 8, 2003).
It means you don't need a special permit, provided you will write a letter of intent in Spanish, renouncing to your vehicle and donning it to the church you are looking for. Also, the document must include the original receipt or invoice for the vehicle.