This would work, right?

Gonna learn this on guitar. No, it's not a lullaby - it's Cheap Trick!  But it seems appropriate to sing to a baby, no?

A G D A
            A                                 A/G#
         I want you to want me
           F#m                            F#m/E
         I need you to need me
              D                               D/C#
         I'd love you to love me
               A                                    A/G#
         I'm beggin' you to beg me
           F#m                             F#m/E 
         I want you to want me
           D                                 D/C#
         I need you to need me
              A                               A/G#
         I'd love you to love me
                       F#m                              B
                  I'd shine up my old brown shoes
                       G                              A
                  I'd put on a brand new shirt
                       F#m                           B
                  I'd get home early from work
                               G                  F#m
                  If you'd say that you love me
                           A                                         E
                           Didn't I, didn't I, didn't I see you cryin'
                                F#m                                      D
                          Oh, didn't I, didn't I, didn't I see you cryin'
                          A                                                             E
                          Feelin' all alone without a friend you know you feel like dyin'
                                 F#m                                              D
                          Oh, didn't I, didn't I, didn't I see you cryin'

         I want you to want me
         I need you to need me
         I'd love you to love me
         I'm beggin' you to beg me
                  I'd shine up my old brown shoes
                  I'd put on a brand new shirt
                  I'd get home early from work
                  If you'd say that you love me
                           Didn't I, didn't I, didn't I see you cryin'
                           Oh, didn't I, didn't I, didn't I see you cryin'
                           Feelin' all alone without a friend you know you feel like dyin'
                           Oh, didn't I, didn't I, didn't I see you cryin'
                                             *Solo*     A E F#m D

                           Feelin' all alone without a friend you know you feel like dyin'
                           Oh, didn't I, didn't I, didn't I see you cryin'

         I want you to want me
         I need you to need me
         I'd love you to love me
         I'm beggin' you to beg me