They made dye just for such things check the paint section at your local auto store.
It's usually called fabric dye or something similar, just watch the plastic windows.
Another alternative is to take just the cloth parts to a laundry mat.
USE COLD WATER, the top will shrink if it's hot.
Toss it in one of the big washers and toss in 2 bottles of black rit-dye.
No soap. Let it wash and rise, then take it out and let it air dry in a shady place not it the sun.
The rit-dye will make it look great if the dye is distributed evenly in the water.
I had a friend who said he mixed rit-dye in with water in a big washtub and then tossed his top in and mixed it around for awhile, left it to soak for awhile (couple hours he said) took it out air dryed and it was good to go.
Never used the rit-dye method but the spray can stuff works pretty good.
I have soft doors I'm about to dye, I can test the rit-dye method and post up the results.