Couples who have money are happier in general. One of the leading causes of divorce is financial issues. Being broke puts a huge strain on relationships and leads to all kinds of disagreements and fights. This isn't true in all cases as I'm sure there are plenty of couples who are broke and happy, but i think generally speaking it rings true.
There are some people that are truly happy without money. In most cases, you need it to get what you want, or at least avoid what you don't. So, logically speaking, couples with money are in most cases going to be happier than ones that don't have any, that's just what the world mandates.
One thing is for sure, having more money in a relationship makes things more convenient. When you're not struggling to get by you are generally happier and tend to enjoy life more fully. With children in a relationship it's an absolute necessity. Couples with more money are able to engage in more leisure activities, which should naturally make them happier.
While I would argue that happiness overall is not tied in with money, money concerns are one of the largest reasons for divorce. Money concerns add stress to a marriage. So if people have enough (they don't necessarily need to be rich), this can help them have something less to argue about. However, money doesn't buy happiness, and people can be happy without it. It's just a problem that is a statistical average, not a guarantee of discontent.
What tends to make couples happy are things like trust, communication, and being on the same page. None of those things can be bought with money. However, a lot of couples fight about money and not having enough of it, so in that regard it could help the marriage. It just depends.
Money can help you in a difficult situation, money can buy a lot of things, but it cannot buy happiness. There are plenty of rich couples who are miserable. There are plenty of couples with modest income, or even poor, who love each other and are happy in each other company.
Money does not directly indicate the happiness present within one's life, and especially couples. I find it actually easier if one is in dire straits and has the emotional support of a loved one. Also, with the presence of another life depending on your actions and decisions, your desire to survive is exponentially increased.