I know of two places.
When I was last there I hired from Happy Biking. They’re Dutch I think, and based near the Tropical Centre bus station in Playa del Ingles. http://www.happy-biking.com/
There is also Freemotion opposite the Faro de Maspalomas bus station. They have lots of shiny new bikes, and it’s a much shinier new set up, but a bit pricier from memory. Their website says they’ve also got a shop at one of the hotels in Playa, but I’ve never investigated that one. http://free-motion.net/en
I’ve also recently found http://www.cyclegrancanaria.com/default.aspx which has downloadable pdfs of mountain bike routes, but not so much for road. I might give some of them a try when I’m next out there (my parents live out there so I visit a couple of times a year).