At the Maclellan Shelter for Families, Gena Roberts Ellis stands in front of about two dozen residents, blending humor with what she views as an urgent mission: helping these families stay intact.

The jovial and freckled Ms. Ellis holds the group in rapt attention as they eat boxed dinners and then settle into rows of chairs set up for a weekly parenting workshop in Chattanooga. A family with two teenagers sits in a corner. A young couple in the front row holds hands; behind them, another couple bounces a newborn baby.

Ellis uses the analogy of a car’s fuel gauge to describe how kids change the family dynamic and why parents need some personal time.

“When we parent on ‘E,’ we’re really not parenting,” Ellis says to nods of agreement from the audience.

For 20 years the organization Ellis works for, First Things First, has been trying from every angle to help lower divorce rates and raise marriage rates in this Southern city with higher-than-average poverty. Staff lead dozens of local workshops that range from teaching high-school girls about healthy relationships, to couples counseling at churches, to classes in jails, for fathers in trouble for missing child-support payments.

The effort is rooted in research suggesting that, despite diverging opinions on the value of marriage in modern society, kids who grow up with married parents are more likely to go to college and far less likely to end up poor.

But across America, it’s proving remarkably difficult to successfully promote more and stronger marriages. Here in Tennessee, for all the couples First Things First may have helped along the way, the effort hasn't reversed what appear to be deeply rooted trend lines. The rate of people marrying in Hamilton County, which includes Chattanooga, declined between 2009 and 2014, and nationally the trend has been downward since the early 1980s. Some positive news, here in Tennessee and nationwide, is that the divorce rate has been declining, yet it remains considerably above 1960s levels. [Editor's note: This paragraph has been updated to correct an inaccuracy on divorce rates.]

This doesn't mean efforts to support and promote marriage are useless, but it suggests that programs like First Things First are at best a partial response. Experts are promoting a range of options, from lowering welfare penalties for joint incomes to building a national public awareness campaign to illuminate the positive effect that marriage has on children.

“There’s a surprising degree of agreement that the country needs marriage,” says Ron Haskins, a senior fellow and co-director of the Center on Children and Families at the left-leaning Brookings Institution. “The problem is that nobody really has a good agenda.”

Marriage rates in the United States have been declining for decades, particularly among the poor and less educated, despite considerable federal- and local-government promotion efforts. But historically, the idea of the federal government telling people to marry has been contentious, and now it has fallen out of favor even among many former supporters.

Ideas that might help

“I’m a fanatic about marriage, but I will admit that we haven’t demonstrated impacts to a degree that we know how to do this,” Dr. Haskins says.

Still, he and other social-policy experts see other strategies that could be pushed, to try to make marriages stick.

One of the simplest, says Angela Rachidi, a poverty expert at the conservative American Enterprise Institute, would be to lower the marriage penalties embedded in federal welfare benefits. She and many others point out, for example, that the Earned Income Tax Credit, a federal tax rebate for lower-income people, is reduced when people marry and join their incomes.

“It’s probably not the government’s role to encourage marriage, but it shouldn’t be in the business of disincentivizing it,” Dr. Rachidi says.

Other marriage and poverty scholars, such as Isabel Sawhill, recommend that Americans focus on preventing unplanned pregnancies among young women by offering easy access to affordable birth control. She knows that’s a politically polarizing idea, but for her the rationale is compelling.

“Fifty percent of all babies born to the youngest generation are born outside of marriage, and overwhelmingly they’re unplanned,” says Dr. Sawhill, a senior fellow in economics at the Brookings Institution. “If we don’t like the idea of unwed parenthood or single parents, then we need to empower these women to be able to use effective forms of contraception.”

There’s also an opportunity, she says, to influence young people to wait until they’re married to have children. It’s an approach that worked for teen pregnancy, points out Sawhill, who helped found The National Campaign to Prevent Teen Pregnancy. The 21-year-old public-awareness effort has contributed to a 55 percent decline in teen pregnancies over the past two decades, and a 64 percent drop in teen births, the nonprofit reports.

The idea is also popular among a bipartisan group of scholars who – inspired by successful teen-pregnancy and anti-smoking efforts – proposed in 2015 a national public-awareness campaign about the positive effects of stable marriages on children.

“In the same way that leading institutions advise us to abstain from smoking, eat healthy foods, get plenty of exercise, read to our children, volunteer, give to charity, wear seatbelts, and finish school, they should advise young people to postpone having a child until they have a stable partner and are ready to be parents,” wrote the group. “For the overwhelming majority, that means marriage.”

Daunting economics

For now, the data on marriage are foreboding. About half as many less-educated, low-income American women marry as do their educated, elite counterparts. Today, 40 percent of children are born out of wedlock, up from 5 percent in 1960.

Against this backdrop, researchers wrestle with chicken-or-egg questions: If more marriages might help reduce poverty, it’s also possible that less poverty would make more Americans marriageable. So, some experts say another way to promote marriage is to help more people get access to education and career opportunities.

The poverty trap for children of single parents was one thing that Chattanooga’s First Things First was trying to avoid when the organization was founded in 1997 by the city’s business leaders. “It’s not that single parents aren’t good and aren’t trying, but there’s only so much to go around when you have one human being,” says Julie Baumgardner, the group’s president and CEO.

Community leaders were alarmed by the local divorce rate, says Ms. Baumgardner, which at the time was 50 percent above the national average. “These businessmen said, ‘This is going to affect our ready-to-work workforce, and ultimately it’s going to impact us as a community,’ ” she says.

First Things First is among the many local efforts that received grants during the biggest federal attempt to stem the marriage decline, under former President George W. Bush. But the Bush-era programs that have been evaluated – from ones in Orlando, Fla., to Wichita, Kan., and the Bronx, N.Y. – were found to have had little to no effect on marriage rates or family stability. (First Things First was not among those evaluated.)

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Though the outcome was discouraging for marriage advocates, they hope for lessons that can inform better marriage programs in the future.

Baumgardner, for one, simply refuses to give up. She says: “The question is: Do we want to sit here and do nothing and let things happen as they will, or do we want to make an attempt to help people do what they’re trying to do?”