Measurements of the suppression of the yield per nucleon of J/psi and psi(') production for 800 GeV/ c protons incident on heavy nuclear targets, relative to light nuclear targets, have been made with very broad coverage in x(F) and p(T). The observed suppression is smallest at x(F) values of 0.25 and below, and increases at larger values of x(F). It is also strongest at small p(T). Substantial differences between psi(') and J/psi production are observed for the first time in p-A collisions. The suppression for psi(') production is stronger than that for J/psi for x(F) near zero, but becomes comparable to that for J/psi for x(F)>0.6.