Use a crochet hook!
Keep the yarn on the underside of your work, insert the crochet hook from right side, down into the stitch, catch the yarn and draw the loop up to the topside; then put the hook into the stitch above, and again wrap the yarn over the hook and draw it up. This produces a lovely, even vertical stripe.
It works even better – on stockinette – if you work a column of purl stitches where the stripe will go. The purl column drops back and the contrast colour lies flat with the top of the knit stitches.