We have studied the B{sup {+-}} {yields} J/{psi}{pi}{sup {+-}} and B{sup {+-}} {yields} J/{psi} K{sup {+-}} decays using a 20.7 fb{sup -1} data set collected with the BABAR detector. We observe a signal of 51 {+-} 10 B{sup {+-}} {yields} J/{psi}{pi}{sup {+-}} events and determine the ratio {Beta}(B{sup {+-}} {yields} J/{psi}{pi}{sup {+-}})/{Beta}(B{sup {+-}} {yields} J/{psi} K{sup {+-}}) to be [3.91 {+-} 0.78(stat.) {+-} 0.19(syst.)]%. The CP-violating charge asymmetries for the B{sup {+-}} {yields} J/{psi} {pi}{sup {+-}} and B{sup {+-}} {yields} J/{psi} K{sup {+-}} decays are determined to be {Alpha}{sub {pi}} = 0.01 {+-} 0.22(stat.) {+-} 0.01(syst.) and {Alpha}{sub K} = 0.003 {+-} 0.030(stat.) {+-} 0.004(syst.).