I did some searching around, but most of the studies I was able to find were pretty old. Here are some things to get you started.
This paper indicates that mothers with large families become happier if they undertake full-time employment (see the discussion on page 615):
- Mothers’ Work Hours and Marital Quality: Variations by Family Structure and Family Size
- Stacy J. Rogers
- Journal of Marriage and the Family, Vol. 58, No. 3 (Aug., 1996), pp. 606-617
- Published by: National Council on Family Relations
This paper indicates that having a larger family size consistently leads to lower levels of happiness on average (see pages 130-131):
- Measures of Economic Well-Being as Predictors of Psychological Well-Being
- Mullis, Randolph.
- Social Indicators Research. Dordrecht: Mar 1992. Vol. 26, Iss. 2; pg. 119
The other studies I found were older.
This paper included a short survey on studies of that sort (see page 760), but it was written in 1977, and most of the studies that it cites are even older. Basically, it confirms what was stated in the more modern papers - that having more children led to a lower level of marital satisfaction on average:
- Familism and Marital Satisfaction among Mexican Americans: The Effects of Family Size, Wife’s Labor …
- Frank D. Bean, Russell L. Curtis, Jr. and John P. Marcum
- Journal of Marriage and the Family, Vol. 39, No. 4 (Nov., 1977), pp. 759-767
- Published by: National Council on Family Relations
The above paper did mention one study that indicated that higher degrees of
child density - that is, the number of children you have, divided by your years of marriage - led to a greater degree of role satisfaction (i.e. how couples feel about performing certain roles within the family) (see pg 437-438):
- Marital and Family Role Satisfaction
- Bruce A. Chadwick, Stan L. Albrecht and Phillip R. Kunz
- Journal of Marriage and the Family, Vol. 38, No. 3 (Aug., 1976), pp. 431-440
- Published by: National Council on Family Relations
And the above paper made reference an article by Judith Laws, 1971 (Journal of Marriage and the Family, August) that they recommended as a good survey on the family size and happiness literature at the time. Though they emphasized that most of what she describes indicates a negative relationship between family size and marital happiness.
I didn’t bother to look into the article by Laws.
So basically, most of the scholarly articles I was able to find indicated that having more children led to less happiness in marriage. Of course, as I pointed out, most of those studies were older. I was not able to find any recent studies that touched on this topic. I do not know if it is still an active area of research. Sorry.