Scientific evidence has shown us that in fact, money DOES buy happiness, but only to a certain point.
A famous Princeton study (linked below) found that emotional wellbeing increases steadily with income, up to around $75,000 per year. After that point, income does not have much of an effect on emotional wellbeing.
Research has previously shown that low income families are more likely to divorce than higher income families (see NCFR link), and that lower income couples were more likely to have their relationship negatively influenced by money problems. Together, these facts suggest that conflict within low income families can often relate to money problems, leading to unhappiness and divorce at higher rates than high income families.
The Princeton study has found that low income families also experience more emotional distress from unfortunate life events (which include poor health and loneliness as well as divorce) than do higher income families.
With that said, it seems clear that $75,000 for a family isn't really all that much money. Two parents earning just over $37,000 per year will earn that much (which works out to around $18 per hour per parent working 40 hours per week). Clearly, though, a single parent earning that salary will earn far below the 'happiness threshold', and will suffer from many of the financial troubles experienced by low income families.
Essentially, I think the data shows us that money can buy happiness if you are in poverty or struggling with money. In this case, the money will eliminate several sources of unhappiness, such as stress and marital conflict over finances. But once you have a comfortable family income: enough to pay for all your fixed expenses (such as rent/mortgage, bills, and groceries) and maybe a few luxuries (movie tickets), money doesn't really have much of an impact on happiness.