I did exactly that last year. Two weeks in Ibiza without any flying seemed a tall order so I went on the hunt for something to fly. (I told the wife I was off to find her something at the shops

)
I had my licence with me so was allowed to pass through into the "Aeroclub Ibiza" area of the airport and then I found a chap called Xavier. A very nice chap he is too. Unfortunately it appears that there is not a club as such and people who fly from there tend to be owners/part owners in aircraft. I was offered a 50th share in a C337 for a thousand pounds and was told I would be more than welcome to fly it as often as I liked!
The Palma/Ibiza airspace is quite complicated too. Therefore, I decided to go and buy some croissants to take home for the wife and gave it up as a bad job!
Good luck