If you're in zone 7 in Oklahoma, if you can find 'Palmetto' St. Augustine, it likely would be cold hardy enough for you. I don't know of any other lawn grass that will give you the look of St. Augustine and its tolerance of part-shade conditions. Depending on what kind of tree you're talking about and how dense the shade beneath it happens to be, even St. Augustine may not grow well in that shade and you might have to use a ground cover in the shadiest spots.

If you're in central OK or southward, even 'Raleigh' St. Augustine might be cold-hardy enough. However, every now and then, an extreme cold spell in winter, like we experienced in 2011, might freeze out your 'Raleigh'. That even happens as far south as Dallas-Fort Worth some winters.

Dawn

Here is a link that might be useful: 'Palmetto' St. Augustine

Zoysia has a somewhat similar look as it is a courser texture than Bermuda. If you insist on a warm season grass I would look at that. It will be available here, I have no idea where you would get St Augustine in OK. Last winter my home in North Edmond got down to -20 F in February. That temp will toast any variety of st augustine.