score:7
I've visited the Canary Islands several times and rented cars from Cicar. It was recommended by a German travel guide (book) as reliable company.
Cicar is a native car rental company and claims to be the largest one on the Canary Islands, with the most offices.
Personally, I had no problems with their cars or their service and would choose them again. (However, I only rented cars three times at different locations) Nice goodie: You get a (simple) map with points of interest and an audio-CD giving some information about that points.
According to Cicars web site, office hours at Tenerife South airport are 7:00-23:00, 7 days/week. But their conditions also state that you can also rent cars outside of their office hours. (See here or goto http://www.cicar.com/EN, click "search", and find the link [see conditions] on the left, below the booking details)
OK, this sounds more like an advertis*m*nt, but I'm just a pleased customer.