I've just purchased a house with an old Genie garage door opener that uses the simple dip-switch remote configuration system (no rolling code, in other words). The garage has two doors, each with its own opener. Given that the size of each opener is roughly the size of a box of cheap cigars, the range is terrible (need to be within ~10 feet), and the remote generally feels like you're going to break it when you push the button, I'd like to replace the two remotes with a single smaller remote. There are a bunch of different options on sites like Amazon, Lowe's, Home Depot, etc., but most of these seem to be geared toward openers with rolling code systems. Will these remotes work with the sort of opener I have? FWIW, the current remote I have is a Genie GT90-1.
I purchased a Chamberlain KLIK1U 2 button universal garage door remote a little while back and remember there being a dip switch option. I'm not sure if you can program two dip switch openers to it, but it might be worth a try.
Another option which is the one I had to do is that if you have a button inside the garage that you press to open the door, you can get a pair of Chamberlain 955D receivers. It allows you to use a rolling code remote on the opener. If you used one for each opener, you could get one remote with several buttons and program it.
I hope this helps!
You probably can change to a rolling code system if you want but this would involve installing an additional board in your receiver unit and would probably be to expensive to warrent doing, the other option is to use a small remote, This page from genie shows the specs of your current remote and you can compare it with a site like this one(this page is just an example go to the home page for all the examples that you may be able to use)