I went to Gran Canaria (Maspalomas) about the same time a few years ago. Sadly didn't find it to be brilliant for birding, though thoroughly enjoyable all the same. Try and get to the Pajonales national park to try and see the blue chaffinches, it's a bit of a difficult drive (I wasn't driving so it was fine!) and we didn't see anything but turtle doves. There are some easier forests and reservoirs and suchlike in the interior of the island, where things such as canary, plain swift, sardinian warbler and berthelot's pipit should be easy. If you're on the coast, check out any rough areas for trumpeter finches. ALWAYS stop to have a quick look at golf courses - oases in most parts (23 hoopoes all together is not to be missed!)
If you're based in the North West, you should see some good things, as it's a lot greener than the South East. If you do go around the island the oasis de
Maspalomas is good, though only practical before all the sun worshippers turn up, here I saw whimbrel, kentish plover (breeding) little ringed plover and one collared pratincole. Cory's shearwaters on the sea.
Admittedly, GC is perhaps the least visited of all the islands, as all of its birds and more can be seen on Tenerife. But it's still a beautiful island and I was more than satisfied with the things I saw.