Is there an inverse co-relationship between the US birthrate and any
general measure of prosperity like GDP? Ideally I would like to be
able to compare the following three periods with each other: 1870 to
1970; 1970 to 1995; and 1995 to 2002.

There are some exceptions, such as a burst of births following wars. I
suspect the burst did not occur following Vietnam and the Gulf war,
perhaps because many of the combatants suffered low level poisoning
and other health problems. I have not seen any evidence to refute the
inverse relation between birth and prosperity in the USA or elsewhere.
  Neil