A difficult question to answer.
The paperwork is so complicated, even for residents. Some friends of mine, who were not residents here, found it so difficult they were married in a registry office in the UK and had a blessing at the church in Los Gigantes followed by a reception locally. You can read the full story on our news http://losgigantes.com/news/?p=576#more-576
The person you need to speak with is Father Keith. He is regularly in Los Gigantes for the church services in English but you could contact him through the church web site http://www.tenerifechurch.com/
Do let us know. It is a question often asked.