Assuming your surfboard is no more than 31" wide the SeaSucker Surfboard Carrier # 298-BX1806 is the only real option. I can understand any hesitation to mount your surfboard with suction cups but they have a pull strenght of 1,260 lbs so they aren't going anywhere. Their demonstration video attached below does a great job showing this as they lift up the vehicle by the rack.
If you're still worried about trusting your surfboard to a carrier stuck onto the top of your car with suction... view full answer...