Opponents of same sex marriage feel that their strongest secular argument is the negative effects such a family structure will have on the well being of children.

The American Academy of Pediatrics yesterday issued a statement saying that it has reviewed all the published studies comparing the children of same sex couples with those of opposite sex couples and concludes that there is no basis for this belief.

The American Academy of Pediatrics (AAP) supports civil marriage for same-gender couples – as well as full adoption and foster care rights for all parents, regardless of sexual orientation – as the best way to guarantee benefits and security for their children.
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A great deal of scientific research documents there is no cause-and-effect relationship between parents’ sexual orientation and children’s well-being, according to the AAP policy. In fact, many studies attest to the normal development of children of same-gender couples when the child is wanted, the parents have a commitment to shared parenting, and the parents have strong social and economic support. Critical factors that affect the normal development and mental health of children are parental stress, economic and social stability, community resources, discrimination, and children’s exposure to toxic stressors at home or in their communities — not the sexual orientation of their parents.

Of the 60 studies reviewed, only two suggested that the children of same-sex couples were disadvantaged.

The American Psychological Association had done a similar study even earlier in 2005 and came to the same conclusion (citations omitted):

Like families headed by heterosexual parents, lesbian and gay parents and their children are a diverse group. Unlike heterosexual parents and their children, however, lesbian and gay parents and their children are often subject to prejudice because of their sexual orientation that can turn judges, legislators, professionals, and the public against them, sometimes resulting in negative outcomes, such as loss of physical custody, restrictions on visitation, and prohibitions against adoption. Negative attitudes about lesbian and gay parenting may be held in the population at large as well as by psychologists. As with beliefs about other socially stigmatized groups, the beliefs held generally in society about lesbians and gay men are often not based in personal experience, but are frequently culturally transmitted. The purpose of this summary of research findings on lesbian and gay parents and their children is to evaluate widespread beliefs in the light of empirical data and in this way ameliorate negative effects of unwarranted prejudice.
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As this summary will show, the results of existing research comparing lesbian and gay parents to heterosexual parents and children of lesbian and gay parents to children of heterosexual parents are quite clear: Common stereotypes are not supported by the data.

What this says to me is that if people really care about the mental health of children of same sex couples, the best thing to do is for communities to reduce parental stress by ending discrimination and accepting such families as fully equal.