Firstly, establish whether the garages are common property or on your title. It might not matter in the end but the question will come up. Grab a copy of your title and see if the garage is on it, or not. If it’s yours, you have a better case. If it’s not, perhaps give up now….
Your next step might be mediation:
The threat of having to actually stick up for their point of view might make them cave.
Do you know if anyone else has a problem with the existing doors? If you can get some other owners on board it might help your case. Think of the increase in value if you had modern garage door technology!
If it were me, I’d play up the “ease of access” (borrow a walking stick for the day of mediation!). I’m imagining that old pull up doors might be heavy and frankly I can’t imagine anyone wanting that over a modern, possibly remote controlled garage door. You could throw in the safety aspect too – much safer to sit in your car and open the door remotely than to have to get out to lift it, leaving your car exposed to thieves or yourself open to personal attack.
Good luck.