Hi,
I would suggest a wall of some sort, that will give you a place to put some fill into the yard, so that you will have a level area. Have some slots in teh bricks, so that the water from the uphill side can drain through the wall.
By having 1" minus gravel near the wall, then replace the top soil above the gravel, so you will be able to plant grass again would be a solution. This would mean taking up about 12" of your top soil, putting it on the side, building the wall, then having a couple large truckloads of gravel put down, then relocate the top soil back to it's original location, yet 12 - 20" higher than before.
For a wall, I would suggest a C shape wall, buried about 18 - 24" into the soil, and curve the center of the C into the uphill section, so any water coming down the hill will curve around the wall. Make the wall about 24" - 36" above ground level, and then bury it on both sides, so that the wall will not have pressure on only one side of it. The downhill side can be a slope 45 degrees, in other words 36" wide fill for 36" of hieght. The uphill side can be steep at first, then level out closer to your parking area.
The other fill material is called "Crush and run" in construction terms. It is a mixture of sand, small gravel, and larger stones that are easy to compact to 2000 PSI - firm enough to use under the foundation of a house. They have to test the soil under the home before pouring a slab, and building the house.
Good luck with the project.
Fred.