I know that Belinda's Studio has done a lovely quilt using velvet, it was so beautiful. The stablizer could be normal tear-away. The main problem you will like to avoid is making hoop marks on the suede so you must lay it on the top of the hoop. A normal needle for embroidery should be fine, but no harm using a microtex one
We have used ordinary school glue stick to secure on top of tear-away.
Happy Stitching
From Bev

I have and I used a sticky tear-away, so as not to cause hoop burns on the fabric. I would use a ball needle since the fibers are a bit longer and you wouldn't want to "cut" them with a sharp.;)

It sounds like faux suede (if its a little stretchy) which I use in nappy-making and as Bev mentioned, you dont want hoop marks. I use a sticky backed stabiliser, but I think I'll try a glue stick & some tearaway next time. I have Crayola washables here for my children anyway. xXx