Helping with paving a dirt pakring space.

The area is a small section between a house that used to be covered in grass it is about two car widths. As the number of our cars grew the less grassy area was needed around the house. The area of grass got worse and worse and now it is pretty much hard dirt. We pick up the dust when we get out and it gets in the house.

I wanted to know what would be the best way to fill in this area without having cement or asphalt poured. I was thinking of putting a tarp over the area and fill it in with gravel.

Anything that is not a hard surface like concrete, asphalt, or pavers is going to make dust. It's mostly a matter of how much dust.

Just about anything is going to require cutting the dirt down at least 8" in order to make a flush transition with the driveway. I would consider putting concrete paver blocks over a sand bed. An alternative to the pavers would be pea gravel, which are small roundish tannish stones about 1/4"-3/8" in size. If you order them with plenty of fines (smaller grained gravel, kind of like coarse sand / dirt) included, the pea gravel will pack down nice and firm.

Excavate the area to a depth of 6-8 inches below what you want as finished grade. spread gravel around to a 4" below grade depth. Form the perimeter you wish with 2x4s (use extra stakes, concrete is heavy). Call local concrete supply company for a truck to come fill this space. Smooth it out and broom the surface.

and having typed all that I re-read your question where you asked "not concrete". plastic sheeting and DGA. (dense grade aggregate). Possibly blue stone, depends on your area.

I wouldn't do plastic sheeting at the bottom as it will prevent drainage. Even fully-compacted traffic bond (i.e. limestone chips with fines) will still be a little bit permeable. However, some kind of soil separator will be needed between stone base and compacted existing subgrade. Look for non-woven geotextile fabric which is thicker than typical weed barrier fabric.

Dry-laid concrete pavers might be easiest. Pick your size / pattern, but make sure the pavers are thick enough to handle vehicular traffic (probably 2-3/4" min.) They're typically set over 1" of sand (for leveling), then min. 6" of compacted stone, then the non-woven fabric, then subgrade. 2x4's can be used as edge restraint, or find some paver-specific edging to hem things in.

Good luck!

I use recycled asphalt for my spaces u Sally free if you pick it up.

Crusting agent.

You don't really even need geo textile cloth if you are pouring 4" or more of stone thickness. Yes it will stop the stuff that is there now from growing but new seed will accumulate in the new stone and require vegetation killer anyway. Spend the money on a good 2" thick crusher run course to start off. Tamp it in good. Wash it in a few times with a sprinkler and then put 2" of mixed 57 and 87 stone down. Tamp it in again and drive over it a lot. Good water permeability and the mixed stone sizes lock it in pretty well.