I use a strap, even sitting down. This always positions my guitar in the same place with no slipping ever.

But, to answer your question more specifically, maybe a small towel over your knee would prevent the slipping.

You can try a classical position. Definitely an option.

Footstool might help too. Basically something to get the angle of your leg to be higher at your knee than your hip.

I always use locking straps. Ever have a strap come free while playing in a standing position and find yourself looking at a cracked guitar neck? Now I’m too old so I sit and play but still use a strap and a foot stool. The stool raises my leg enough that the guitar stays put fairly well. It may slip a little (I’m retired so I wear lounge pants around the house a lot and they are slippery with a guitar) but not enough to interfere. I adjust the strap to keep it in place and off I go, hacking out a song, wishing I had some talent. I would like to take this time to make something clear. My brother accused me of sitting around the house in my pajamas. They are LOUNGE pants, not pajamas.

Definitely agree with Michael – a strap is a must even when sitting. As he said, the guitar will always be in the same position once the strap is adjusted to your specs.

When I saw Dire Straits many many years ago (1992), Mark Knopfler had a towel close by throughout the show; true it wasn’t on his knee but somehow I doubt that Mark would have hesitated to have it on his knee if it was necessary.
Mark was the epitome of cool in that show and every time that I saw Dire Strait play live – obvious that he just didn’t care so if you need to use a towel, don’t worry about what others think