Double-knit fabrics wear like iron. It's best to tie that type of quilt.
If they are thin knits that are going to stretch on you, I can recommend nylon tricot as an iron-on stabilizer. Many stabilizers make the fabric too stiff; nylon tricot is better than most.
I have never worked with knit fabrics, but I would think you could also make a quilt with them using a foundation technique -- either muslin or paper.
In any case, you don't want to try an intricate pattern. I would try to keep the pieces large -- perhaps all squares with sashing -- and plan on tying the quilt. Warm n Natural is good for tying because it is very stable and the ties don't have to be too close together.