  We have calculated high temperature series to 12th order in inverse
temperature for singlet superconducting correlation functions of the 2D t-J
model with s-, d_{x^2-y^2}- and d_xy-symmetry pairs. We find the correlation
length for d_{x^2-y^2} pairing grows strongly with decreasing temperature and
develops a broad peak as a function of doping at T/J=0.25 for J/t=0.4. The
correlation lengths for s- and d_xy-symmetry remain small and do not display
peaks. Antiferromagnetic spin fluctuations at low doping act to suppress the
d_{x^2-y^2} and d_xy superconducting correlation lengths. Our results support
the hypothesis that the strong electronic correlations found in the CuO_2
planes of high temperature superconductors are the origin of the
superconducting order.
