I have flown there a few times (2-3 years ago) with a mob called "Lanza Air" whose base is on Lanzarote but who also flew as a flying school and as a banner towing mob from TFS.
http://www.lanzarote.com/lanzaair/index-en.html
They had 2 172s one a simple 172 K and the other a 200 HP with a wobbly prop.
I don't know if they are still there though. Try an email .. they may even be prepared to fly an aeroplane over to you if 2-3 hours are in prospect (I think they had to go to Lanzarote to get Avgas when I was there). Their manager was an English guy called Ed Winsor but knowing those islands I doubt he is still there.
If all else fails try the contact us section of AENA at TFS, which gets the information desk, they were quite helpful.
There are no other airfields I am aware of on Tenerife other than Los Rodeos, which I have flown up to but always found it IMC when I've arrived. I don't think it has bben VMC since 1973.
They may however have schools there if there is nobody at TFS. The other thing to know about TFS is that it gets devlishly windy in the afternoons (all that dark rock being heated by the fierce sun and giving brisk on shore breezes) and so if you do get to fly, arrange it for the morning because it may well be outside crosswind limits from about noon until after dark.
Dave