Don't think you stand a hope at Palma International, however Son Bonet (LESB) is about 5 miles North West and does have a club (at least did last time I was there).
Try
here for an outfit that rents German registered Cessnas and Pipers.
Alternatively try Sloane helicopters at Sywell. They have a base at Son Bonet and might be able to point you in the right direction.
Lastly, a possibly out of date phone number for Son Bonet is +34-971-600151.
Happy hunting.