With a data sample containing 1.1 x lo5 J/$ -+ /L+/L-decays reconstructed with 16 M~V / C ' rms mass resolution, we have measured the differential cross sections versus Feynman-x, rapidity, and p~ for the production of J/$ and 4' in 800 GeVlc p A u collisions. Our results are compared with leading-order QCD predictions and with previous measurements. While the shapes of the cross sections are in qualitative agreement with QCD predictions, the magnitudes disagree by factors of 7 ( J / 4 ) and 25 (4'). Assuming an appropriate form for the differential cross sections in regions not measured, we derive a total J/+ production cross section a ( p + N + J/$ + X) = 442 f 2 i 88 nb/nucleon and a (model-dependent) total 4' cross section u(p + N + $' + X) = 75 f 5 f 22 nblnucleon. For J/$ produced at central rapidity, du(p + N + J/$ + X)/dyly=o = 230 i 5 f 46 nb/nucleon. PACS number(s): 13.85. Ni, 24.85.+p, 25.40.Ve