I happen to have a backyard of poa supina, it was planted in September 2011 in my very shady back yard. I have found supina to be very shade tolerant, but it does require at least an hour or two of direct morning sun to live, 3-4 hours would be better. In areas of no sun it will be thin and weak, and you will have areas of brown or no grass. You will also have fungal issues in periods of wet, cloudy weather. It also requires frequent mowing as it does best between 1-2 inches. Poa supina is an alpine grass, so it doesn't do very well in hot climates. I live in coastal CT, it might have a tougher time in Virginia due to your hotter climate. The good thing about supina is it wakes up very early in the season, and spreads like mad before the trees leaf out, and again in the fall after the leaves drop. Any voids I had this spring were filled in by the end of April this year. My advice for your situation is to keep cutting trees until you get 3-4 hours of direct sun in the summer, and use some of the more shade tolerant tall fescue cultivars.

Do what tiemco said and break out the hammock.

Oh and no tilling. That will ruin the surface of the lawn for 3 years.

Impossible for me keep cutting the trees, I did all I could on my property. All the others are not mind. This has become very frustrating. Any other advice? I was thinking about putting in artificial grass.

Nothing wrong with artificial grass :( put to do it correctly it is $$. Like $6-$9 a sqft

Fine Fescues will work in your back yard as well, some can live in the shade with under an hour of sunlight.

You can go with a blend or a single cultivar. If single cultivar, be sure to use a Strong Creeping Red Fescue.

I'm down in Raleigh and Fine Fescues work pretty well around here when grown in the shade.

Csingh, did you ever get a lawn to grow? I am asking because I have a spot in our backyard that the dogs have completely destroyed and I am considering artificial turf for that area and you also mentioned that. I am in VA, too-northern VA.