I know a balalaika and domra orchestra where almost everybody holds their instruments in place using cut pieces of a common type of non-adhesive non-slip rubberized shelf-liner material, like that in this photograph.
You can buy a roll of this for a few dollars in any grocery or hardware store.
I have used this material myself when I was learning how to hold my new bass viola da gamba in the proper position between my thighs and calves. (the viola da gamba's body is similar to the cello but it has no end-pin to rest on the ground.) But after some practice, I can hold the instrument in the proper position without needing the grippy rubber material.
By the way, I would hesitate to leave this material in contact with a musical instrument for a long period, such as while storing the instrument in a case. I worry that, long-term, the rubbery material might decompose and adhere to or damage a wooden instrument's lacquer finish. But all indications are that this material is perfectly safe for use while the instrument is on your lap.
I remember now that some of my acoustic instrument-playing friends use a loose piece of rough-milled suede leather, which might provide some "traction" due to the rough texture. Suede seems to be most popular with violinists or violists who want some extra cushioning between their instrument and the chin or collarbone, but I think other musicians also use it to help position an instruments on the lap as well.
I went looking for examples of this in photos on the Net but couldn't find anything suitable.