Success! I ran into the same issue as the OP. I just moved into a house in Florida and the previous owner was sketchy, didn't leave any remotes. Real estate agent wasn't able to get them.
The garage door opener is on the older side, but the keypad is wireless. Initially I took the keypad off the wall and tried to use it to program the Tesla, but that failed. The problem (I think) was the keypad only sent a burst signal and it wasn't long enough for the Tesla to recognize. This was true even when I held down the enter button.
What ended up working was reprogramming the keypad PIN. The instructions on the pad said to press the learn button on the garage, enter the new code on the keypad and HOLD DOWN the button on the keypad until the garage blinked. So I put the Tesla in learn mode, pressed the learn button on the garage, typed in my new pin on the keypad and HELD DOWN the enter button on the keypad while standing in front of the bumper. The garage recognized the new pin right away, but I continued to hold down the button and 5 to 10 seconds later it too registered the signal. Now I'm good to go!
tl;dr If you garage has a wireless keypad, use the set new pin functionality to send a continuous signal to the Tesla from the keypad.
