I divide dwarf dianthus on my nursery shortly after flowering which is usually mid June. You can divide them as late as mid july. I've not tried cuttings but I understand they take easily and I would suggest June/July would be a good time.

If you don't want many I'd stick to division as the plants will be much bigger and should be a decent size next year. I divide one litre pots of dwarf dianthus 4-5 ways. and by the following flowering season they're as big as the parent plant was before division.

Thank you Anchorman, that is a great help and a very full answer...... it looks as if I will have to leave them until next June/July