Civil Liberties

http://en.wikipedia.org/wiki/List_of_Justices_of_the_Supreme_Court_of_the_United_States

the chart isn't laid out in a way that's easy to answer your question, but it looks like we had a majority in 1969 (based solely on the president's party affiliation), and lost it with fortas's resignation and replacement with nixon's appointment of blackmun.

for 1969 it was:

black (fdr)
douglas (fdr)
white (jfk)
fortas (lbj)
marshall (lbj)
----
harlan (dde)
brennan (dde)
stewart (dde)
burger (rmn)


that said, party affiliation of the president doesn't always indicate the leaning of the justice, or at least it didn't. around that time. nixon's appointments in particular covered a wide range of the political spectrum.