You should be able to grow one or more varieties of blackberries if you have at least 200 or more chill hours during the winter. Probably the easiest thing to do though would be to go to a local nursery and ask them for advice since they probably have the most experience in your climate.

Check out bob wells nursery. They're a Texas nursery that I've been using (I'm assuming you're in Texas???). They're very helpful, you can call and ask about suitable plants for your area. Blackberries and blueberries are an excellent option for zone 9a; they do well here in Texas. I also am in zone 9a and am new to growing fruit. The main thing is, at this point, you should probably wait till fall to plant a bare root anything. Potted plants should make it, even if planted in the dead summer heat.

I'm not sure if you're into trees; figs, plums, mayhaws, citrus and loquat do well here. Anything you want to plant, research it's chill hour requirements!

2-3 hours of sun is going to be your issue more than the heat. That said, what sun you get is going to be strong, so maybe that will make for more success than it would here in Oregon.

I grow strawberries (regular not alpine) in what is more shade than recommended and they do fine, maybe not as sweet as they could be. I also have gooseberry and hardy kiwi in a lot of shade, just don't know if they would like it in Texas.

Thank you so much for your replies! I will definitely wait until fall to plant. I don't think we have the space for trees unfortunately. Sounds like strawberries and maybe blueberries or blackberries are my best bet.