As already stated there is/was a 172 available in Lanzarote.
I can also tell you that Aero Club Gran Canaria are based at a small strip just outside San Augustin (near the Go kart track) and you can also rent PA28-180's from there. It is directly on the extended centre line of LPA and LPA airspace starts at 1000' above it.
I lived in the Canary Islands for quite a while and during the very late 80's I had a Spanish rating added to my CAA PPL which allowed me to fly solo Spanish registered aircraft. I still had to do a couple of hours Club checkout and the Club strip was exclusively Spanish RT but it was worth it.
Having said that, there are not really a lot of places to fly GA in the Canaries aside from island to island and I know it is just a personal opinion but those water crossings just don't appeal to me at all.
I would say take an accompanied sight seeing flight, but solo rentals - with the complications of being checked out and the possibilities of anything other than a 'round the island' flight may make things a little complicated
Good luck
tony