The invariant yields for $J/psi$ production at forward rapidity $(1.2<|y|<2.2)$ in U$+$U collisions at $sqrt{s_{_{NN}}}$=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 $cbar{c}$ coalescence. Two different parameterizations 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, $N_{rm coll}$, and these were found to give significantly different $N_{rm coll}$ values. Results using $N_{rm coll}$ 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 $cbar{c}$ coalescence becomes more important than the decrease in yield due to increased energy density. For midcentral collisions, the conclusions about the balance between $cbar{c}$ coalescence and suppression depend on which deformed Woods-Saxon distribution is used to determine $N_{rm coll}$.
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