This post, which discusses layering, has the information you are looking for. I find that it is much easier to work with the Dianthus in large pots. Remember the plants must be done blooming and the new stalks must be soft. Review this post:
Attached is a photograph of one purple Carnation cutting which I rooted and which flowered indoors on 2012-02-19 only to die a month later from root-rot. I will be posting more on this later but I mention it here to show that even cut Carnations can be rooted but it is extremely difficult if the stalks are not soft. For now, my best advice is to stick with layering.