The passive equivalent of '(I) (like) (to sing my baby sister to sleep)' is '(To sing my baby sister to sleep) (is liked) (by me)'. '(My baby sister) (likes) (being/to be sung to sleep) (by me)' is active voice, as you can see from the main verb 'likes' (passive voice needs verb [be] and a passive participle main verb). 'Singing my baby sister to sleep is something I like' is also active voice.
The problem is that there are two verbs here - 'like' and 'to sing', both of which could be turned into passive, 'like' easily and 'to sing' with great difficulty. The passive voice equivalent of '(to sing) (my baby sister to sleep)' is '(my baby sister) (to be sung to sleep)', so whole sentence would be 'I like my baby sister to be sung to sleep by me'.
Both of these passive voice sentences are at best extremely awkward and at worst completely ungrammatical (I can't decide), so the best reasonable equivalent is 'My baby sister likes to be/being sung to sleep by me'. (There are other choices.)