Here is a copy of the doubled over neckband I use on my machine knit sweaters. I use it with my cut and sew necks.
I knit two backs of a sweater (this saves time on shaping) and then I cut one for the front. I sew with a zig-zag stitch and when I am happy with the shape, I cut the neck. Then I sew one shoulder and hang the neck stitches onto the machine, right side facing. Then I follow the instructions for doubled over neckband. I makes a really nice stretchy band so there is no need for buttons on the side of a child's sweater.
Here are the instruction from Glynne Jones
Doubled over Neckband with a stocking stitch border
After joining one shoulder, with RIGHT side of garment facing you, pick
up around the neck on to main bed (rough estimate of No. of stitches
required is the No. you cast on for the back).
Knit 3 rows stocking stitch at MT-1. Raise ribber, transfer stitches to get
the rib setup you want, hang comb and weights.
Knit enough rows to double over the band (I 'guesstimate' the number by
folding over the welt and seeing what looks 'right'). Transfer sts to main
bed, drop ribber down and remove combs etc.
Pick up last row of stocking stitch so that neckband is folded up. Knit 4
rows stocking stitch, one row nylon cord, several rows of waste yarn and
strip off from machine.
After joining second shoulder and sewing seam of neckband, pin down the
stocking stitch flap and backstitch through stitches in last row of main
yarn (use blunt tapestry needle and you won't need to remove waste yarn
until after you have done all the backstitching). Work the backstitching
into and out of each knitted stitch so that there is a little 'bar' between