What stabilizer do you recommend for computerized embroidery on knits?

One option is to adhere Sulky Sticky to the bottom of your outer hoop and gently press your fabric to the Sticky without distorting it. No need to use the inner hoop. Depending on the stability of the knit, you may need additional stabilization under the hoop. You can spray Sulky KK 2000 Temporary Adhesive Spray onto Sulky Tear-Easy Adhesive and add as many layers as needed under the Sticky.

Or, you can use Sulky Tear-Easy in as many layers as necessary (probably at least three), hooped with the fabric. After stitching you can gently pull each layer of Tear-Easy away after stitching without harming the embroidery stitches. Again, I would use the KK 2000 to create a firm "sandwich" of the Tear-Easy. This keeps the needle from having to deal with layers, since it essentially becomes one layer, and it helps avoid "flagging" of the needle and skipped stitches. Also, professional embroiderers have told me that they like to criss-cross their Tear-Easy, one piece going one direction and the next piece going the other direction.

Many people have switched to permanent "cut-away" type stabilizers for knits. With a cut-away stabilizer, the stabilizer remains behind the garment and helps to stabilize it through washings. (You know how embroideries tend to "ball up" after washing? This permanent stabilizer helps to prevent that.) We have two permanent stabilizers, the first, Sulky Soft 'n Sheer (which would be my preference for knits) is very soft, soft enough for a baby's skin, and can be layered in as many layers as the fabric requires. (This is not a hard and fast rule; since some knit fabrics are more stable than others, I would always do a test on a scrap first. Once you've gained some experience with this, you will know by feeling and looking at the fabric how much stabilization it will need. Always error on the side of too much rather than too little.) Our other permanent stabilizer is Cut-Away Plus, which is heavier and more suitable for sweatshirt-type knits. Both these stabilizers remain behind after stitching, and are "cut-away" leaving a small allowance around the design in the inside. Check out all of Sulky's Cut-Away Stabilizers.