Lap bowls, and supported spinning.
Was spinning fine singles on my usual pretty blue and white china bowl, and decided that I didn't want to risk loosing it slipping off my lap. Scrounged two other alternatives, one is glass cover to a thrift store jar, and the other is a bit of translucent marble (?) stone with a dimple in the center of it (I think these are used as little stands for polished stone eggs and crystal spheres - long ago yard sale purchase for 25 cents).
The latest commercial solution seems to be fixing the bowl to a little bean bag sort of pillow (see Straddlecreek Spins), but the whole thing to me still looks unstable. I spin mostly on my knee, and wouldn't use a bowl at all, but the point will drill holes in your clothing. I sewed a wooden diz to a bath towel, and that was very secure on the lap, but diz's come with holes, much as I would have otherwise liked that solution - also, being my only diz, I'd like to keep it free for it's intended purpose of drawing out slivers in roving.
I'm thinking of making a little mat, roughly the size of a generous pot holder. so the base edges of these spinning surfaces like the bit of marble, and the glass lid, can be tucked directly into flaps or a drawstring as part of the mat. Then, the mat can be pinned onto a lap rug of sorts (like the bath towel) for extra stability. Felted wool would be pretty, with crazy quilt style embroidery, paisley applique, and little mica mirrors. Given that I never finish quilts or afghans because I hate working with any projects once they get much bigger than a bath towel...well, I have several to choose from.