How to find closest AppleCare service provider
You can use http://www.apple.com/buy to find a reseller or for third-party AppleCare support. For the Canary Islands, you could use http://www.apple.com/es/buy; either open a UK/US version of the same page side-by-side, or use Chrome to translate it.

In any case, I can see a result when searching /es/buy/ for "Canary Islands" under "Servicios":

UNIVERSOMAC, S.L.
ROBAYNA, 13, LOCAL IZQ
38003 - SANTA CRUZ DE TENERIFE
Tel. +34 922 226 086
Authorised Training Centres
Apple Authorised Service Providers