|Deepika wrote a good tip (see url, above) for narrow bindings that worked well for me on most knits, but I was having fits trying to use it on a sliky knit. After lots of hours of trial and error, here is how I got it to work, and it is so even that I was able to use a black binding on a red knit with good results.
Serge the raw edge where the binding will be placed. Using a large tapestry needle (blunt end), thread clear elastic through the threads of the serged area.
Cut the binding fabric at least 1" wider than Deepika suggests. When applying the binding, the elastic will provide a little bulk so the binding has some body, and better seam recovery -- compensating for slinky's tendency to stretch. The serging makes it easier to hold the elastic in place, and makes getting a uniform width easier.
When applying the binding, have the binding fabric on the bottom, and the main fabric offset from its edge by about 1/8 ". This lets you see the both fabrics and ensure they don't slip out of place. Use the line of serger stitching as a stitch guide. You will be able to see it, because it is on top. After stitching, trim away the binding fabric that will be encased so the unserged edge is narrower than the serged edge.
Wrap the binding fabric around the serged edge, pinning in the flat next to the bound area to keep the fabric from slipping while you are stitching and to hold the binding at the desired width. After stitching ( in the ditch or on the binding) trim away the rest of the excess on the inside.