I don't know (and frankly I don't care) whether such statistics exist, but it seems like if you're trying to show whether marriage does or doesn't provide more stability, you'd have to compare the divorce rate to the rate at which nonmarried, committed couples break up. Marriage obviously isn't a 100% indicator that you've got long-term stability with one person, but it's probably a better indicator, numbers-wise, than not being married.
This is obviously from the UK, but I don't think that really matters.
http://www.ifs.org.uk/bns/bn107.pdf
A number of recent UK papers have documented the association between
marriage and relationship stability. Using the Millennium Cohort Study (the same
data source that we employ in our own work), Benson (2009) finds that around
27% of couples that were cohabiting when their child was born have separated
by the time the child is aged 5, compared with 9% of couples that were married
when their child was born.
Kiernan and Mensah (2010), also using the same data source, document more
detailed trajectories of couples that are married or cohabiting when their child is
born.6 They find that 88.1% of parents who were married at the time of the birth
of their child are ‘stable’ at least until their child is 5 years old, while 2.1%
experience periods of separation but are together when their child is aged 5,
7.6% are lone parents when the child is aged 5 and 2.1 % have re-partnered. By
contrast, around 66.6% of couples that were cohabiting at their child’s birth are
classified as ‘stable’ at age 5 (43.4% remain cohabiting and 23.2% get married),
5.7% experience periods of separation, 20.5% are lone parents and 7.3% have
re-partnered.