South airport you have no hope. The north airport as a flying club called Real Aeroclub de Tenerife (as mentioned above). Fairly acceptable price of around €230/hr with instructor, can't remember if that was C172 or PA28 price. But don't forget the €50 landing fees, but it's dirt cheap considering it's an international airport.
There's also AeroTec, but this is a commercial flight school rather than a club.