This scholarly article answers the question and more
“Family Values”: The Uses and Abuses of American Family History
Elaine Tyler May
(more or less)
https://www.cairn.info/revue-francaise-d-etudes-americaines-2003-3-page-7.htm# (the article is in English)
It doesn't actually state when the phrase itself was first used, but the 'concept' behind the phrase (the phrase strikes me as being vague and meaningless, so I don't think there actually is a 'concept.')
"In 1980, Ronald Reagan won the presidential election promising to restore Americans’ pride in their country and faith in their leaders. Using the rhetoric of “family values,” Reagan shifted the relationship between the family and the state once again, placing the responsibility for society’s welfare on the family, and retreating from the policies of Franklin Roosevelt and Lyndon Johnson. Under Reagan, many of the New Deal welfare state programs were cut back or dismantled. As in the days of Theodore Roosevelt, bad families took the blame for social problems ranging from crime to poverty, and the government backed away from its prior commitment to helping families in need. Derogatory stereotypes, from “welfare queens” to “deadbeat dads,” reflected the prevailing notion that citizens’ responsibilities to society were tied to their family roles. According to Reagan, threats to the nation emerged from feminists who allegedly shirked their domestic roles, and welfare mothers (usually represented as black, even though most women on welfare were white) who eschewed marriage in favor of the dole. The antidote, once again, was the nuclear family. By the 1990s, the pendulum had swung back from society’s responsibility for the family, to the family’s responsibility for society. At this point, “Family Values” landed at the center of the national political battleground (Stacey)."
Prior to this paragraph is the mention of Nixon's related "Silent Majority", but Jerry Falwell's 'Moral Majority' is not mentioned. The swinging of the, especially Southern Baptist vote, from supporting Jimmy Carter in 1976 to supporting Ronald Reagan in 1980 is one of the main reasons Carter lost by such a landslide in the electoral college.
I don't know if Reagan specifically used the term 'family values' during or after the 1980 election campaign. However, I do remember that the tax cuts at that time were sold in part as being 'pro family': "Tax cuts will allow hard working Americans to work less and spend more time with their families.'
Of course, tax cuts were also sold as boosting economic growth: "tax cuts will allow people to keep more of their money and thereby encourage them to work more."
Of course, from an economics perspective, both can be true. The first is called the 'income effect' the second is called the 'substitution effect' (substitute leisure for more work) however, how both could be true for the same person was never explained (it can't be true.)
Also not mentioned in the article is that in the second term of the Reagan Presidency, America's self appointed moral czar, Bill Bennett, was appointed Secretary of Education, and I'd be surprised if he didn't use the phrase 'family values' at least once a day publicly.
