I am sorry for this delayed reply to your gardening question. The spring rush has brought a deluge of questions and we are working hard to catch up!
I would consider a zoysia, most likely the varieties Pallisades, JaMur or El Toro would work fine. They can take shade pretty well but doing some tree trimming to brighten the shade a little would help.
Thanks for the question. Best wishes for a wonderful gardening season. Please stop in again soon!
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