Most research on subjective happiness has found that education doesn't make any difference once you control for income. That is, if you compare two people with the same income but different amounts of education, there's no tendency for the one with more education to be any more (or less) happy than the one with less education.
Of course, you can follow John Stuart Mill and say that more educated people are better off in some sense even if they aren't happier ("better to be Socrates dissatisfied than a fool satisfied." ) But there's also a question of how best to measure subjective happiness or satisfaction. A few surveys have included a series of questions about whether you've felt various emotions in the last few weeks, specifically:
1. Particularly excited or interested in something
2. So restless that you couldn't sit long in a chair
3. Proud because someone complimented you on something you had done
4. Very lonely or remote from other people
5. Pleased about having accomplished something
7. On top of the world
8. Depressed or very unhappy
9. That things were going your way
10. Upset because someone criticized you
The even-numbered ones are generally regarded as bad and the odd ones as good. I regressed reports about each of these on income and education (data from the US sample of the 1990 World Values survey). Here are the results: I give them so that a positive sign always means a favorable effect (more likely to report feeling a good emotion or less likely to report feeling a bad one), and standardize the coefficients for income and education so that they can be directly compared.
Excited or interested .117 .179
Restless .041 .003
Proud .090 .039
Lonely .105 -.035
Pleased .060 .090
Bored .087 -.029
Top of World .064 -.012
Depressed .090 .038
Going your way .094 .051
Upset -.044 -.010
TOTAL .714 .313
For anyone who wants to calculate statistical significance, the standard errors are about .030. In general, these results show that education has a positive effect on experienced emotions. The estimates are larger than those for income (and highly significant) for two: particularly excited or interested in something, and pleases about having accomplished something. There are some negative estimates, and while none are statistically significant, a couple are large enough to be of potential interest: bored and lonely. The contrasting effects for bored and "excited or interested" aren't necessarily contradictory: more educated people might be able to get more deeply engaged in things, but also more likely to become bored when in a situation which doesn't present many opportunities.