Nanking is not a sweet cherry; it's a bush producing tiny little fruits, and actually, is more closely related to plums than to cherries.
That said, I would expect sour/pie cherries, like Montmorency, North Star, etc. to *maybe* work for you (but sweet cherries, not at all).
You say 'sapling' - are you getting grafted selections from a reputable nursery, or just random seedlings from somewhere? Stonefruit rootstocks vary in their requirements for soil type and moisture tolerance - if you're planting grafted/budded selections, perhaps they're not on the appropriate rootstock for your area, or, perhaps you're overwatering, or, perhaps, cherries just won't grow where you are.

But there's a lot of "Zone 7" stuff that is very marginal here due to our hot summers. Just because we get enough chilling hours doesn't mean our climate is right overall. We basically need plants that can tolerate zones 7 AND 8.

I personally would not invest the space, time and money in cherries in Alabama, divine though they may be. (I had a Rainier cherry in northern California. 100% wow.) If you want additional sort-of cherry production like Nanking, you could try the Prunus japonica x Prunus jacquemontii crosses ("Jan", "Joel" and "Joy") grafted onto plum rootstock. Still not a great bet, IMO.

Goumi is also reported to be cherry-like, but I've never tasted one.