One could classify these attempts as follows.
(1) Prudential consideration of consequences.
One can't predict the long-term damage to children, society etc. that this kind of change will bring about, especially when research studies point towards a married father and mother as the most stable setting for children. Very well: but here the battle has been lost long ago, and in the Church as well as in society at large. What about the changes to the law in the last 40 years, with no-fault divorce? What of widespread cohabitation, with its destabilising effect upon children and the idea of the sanctity of conjugal relations? What of the use of artificial means of contraception and what this has done to perceptions of the use of one's body? Surely here what we are witnessing is another blow to marriage among many, which although it will likely affect a very few directly (I'm not denying that symbolically, it is a huge shift) has been preceded by blow upon blow, and which most "mainstream" religious denominations have said or done little about? And, as with all such consequential arguments, when the opposing ideology perceives themselves to be on the moral high ground, they are quite simply ignored.
(2) Pointing out of incoherence.
A lot of the arguments for the change in the legal definition of marriage have been attacked as incoherent: for example, the Bishop of Aberdeen pointed out that the argument that "they love each other, so they are entitled to marry" would work equally well for allowing incest. True: but it was inevitably misrepresented in the press as "Bishop says homosexuality as bad as incest". One will simply fail to communicate one's message, especially when it is a logical message, if the press are illogical.
(3) The "natural" purpose of marriage.
Here we get into reasons for marriage (one of the "natural" ends of marriage being consummation open to procreation, and therefore necessarily between a man and woman). But I think that the notion of "natural" as in "natural law" has so lost its meaning for most people in the English-speaking world as to be misleading. Equally puzzling for them is the related notion of complementarity between man and woman. There is a divorce of body, personality and the psyche in modernity that means such arguments lack cogency. I think this is partly due to a weakness in the whole natural law account of "human flourishing" as the end of human activity. More on that presently.
(4) Divine command.
Interestingly, even liberal churchmen are being forced to say the unthinkable and mention the uncompromising words of Jesus or (even worse) St Paul, in their explanation of the meaning of marriage. This is sometimes a falling back on the last defences, though, a fear that the churches will be coerced into allowing the newly defined marriages to be performed in their buildings, by their clergy. Oh no: we are Christians and Jesus said this and that. As such, these arguments aren't likely to be aimed at persuading the hearers if the audience is a non-Christian public, they are more of a plea for tolerance. When they are sincerely meant by more traditional churchmen to smite the consciences of their hearers, of course they aren't reported in the popular press unless to point out their fundamentalist bigotry, usually backed up by an opinion from an ultra-liberal cleric talking about how terrible it is to misappropriate Jesus and St Paul in this way.
So all in all, I would say that there isn't (apart from valiant but largely hopeless attempts to explain natural law to the general public) any clear, positive exposition of marriage getting through. I suppose large numbers of Christians opposing the change are still in shock at the pace of the change, the apparent sudden intolerance of what 15 years ago would have been "normal" belief, and the hostility towards their attempted explanations of what marriage is about. I don't know how this can be tackled: I think that the whole notion of marriage is so eroded, even among nominal Christians, that the public argument was lost before it started.
My question is a different one than the question of successfully presenting an argument in the press. What is the underlying significance and end of marriage? Partly because it is such a many sided, an all-encompassing thing, it is (a point made by G.K. Chesterton) easy to attack from any angle, but difficult to defend. What I shall try to present in the next post is a sacramental and Neoplatonic idea of what marriage is about; and I don't think that the account of marriage is complete or convincing without such an explanation. This fits into an instinct that I have more generally, that natural law accounts of morality do not go far enough: one needs to explain the transcendent significance of moral acts to make sense of them. I haven't been able to formulate this view very clearly yet into a coherent theory, but I shall try to give some idea of what I am driving at in the next post.