The invariant yields, dN/dy, for J/psi production at forward rapidity (1.2 < vertical bar y vertical bar < 2.2) in U + U collisions at root S-NN = 193 GeV have been measured as a function of collision centrality. The invariant yields and nuclear-modification factor R-AA are presented and compared with those from Au + Au collisions in the same rapidity range. Additionally, the direct ratio of the invariant yields from U + U and Au + Au collisions within the same centrality class is presented, and used to investigate the role of c (c) over bar coalescence. Two different parametrizations of the deformed Woods-Saxon distribution were used in Glauber calculations to determine the values of the number of nucleon-nucleon collisions in each centrality class, N-coll, and these were found to give significantly different Ncoll values. Results using N-coll values from both deformed Woods-Saxon distributions are presented. The measured ratios show that the J/psi suppression, relative to binary collision scaling, is similar in U + U and Au + Au for peripheral and midcentral collisions, but that J/psi show less suppression for the most central U + U collisions. The results are consistent with a picture in which, for central collisions, increase in the J/psi yield due to c (c) over bar coalescence becomes more important than the decrease in yield due to increased energy density. For midcentral collisions, the conclusions about the balance between c (c) over bar coalescence and suppression depend on which deformed Woods-Saxon distribution is used to determine N-coll.