Per Buckles and Hungerman (2013), footnote 5:

We use IPUMS data from 1960 (1% sample), 1970 (the 1% Form 1 and 1% Form 2 state, metro, and neighborhood samples), and 1980 (5% sample). In each Census year, the unit of observation is the child, and our sample consists of children ages 16 and under living with their biological mothers.

The extracts here are randomly selected subsamples of 1,000,000 observations each of the 1970 and 1980 files, which had contained 3,932,376 and 2,766,122 observations respectively, and the complete 578,733 observations in the 1960 file.

Census data are distributed via IPUMS.

sex = sex of child
birthyr = birth year of child
birthqtr = birth quarter of child (1 = Jan-Mar, 2 = Apr-Jun, etc.)
white = child is white
momed = mother's education in years
momhs = 0/1 mother has attained high school degree
momage = mother's age at birth of child
mommarried = mother is currently married
poor = child (and mother) are living in poverty, Census definition(?)

These data are available at https://dataverse.harvard.edu/dataset.xhtml?persistentId=hdl:1902.1/22047