"It's between consenting adults" works well as a legal argument, and I'm pleasantly surprised to see at least some posters restraining themselves to using it as one, but as a moral argument it's too presuppositional of a generally libertarian and individualistic moral framework to convince anybody who doesn't share those presuppositions.
I'm far from a libertarian, whether from a political or from a moral standpoint, but when it comes to the issue of premarital sex I still have trouble finding it immoral for this reason.
Immoral is a strong word. For someone who is not a Christian (or Muslim, or Orthodox and Orthoprax Jew - but I think Jews would overall be less likely to emphasize the immoral aspect of it-), consent just seems the most logical basis on which you can judge the morality of it.