Yes, there are such songs.

It was once a "bench-mark-requirement" that a child "master" the multiplecation-tables in order to be promoted from 4th Grade.

My brother had a terrible time (as terrible as my experiences with spelling....(which if such a requirement existed I would still reside in a forth-grade-classroom.))

Therefore, my parents invested in a series of records....the times-tables, up to twelve. They got my brother through the test. (Good, Lord knows, you don't want to know what his job is TODAY!)

Use a I,IV,V progression and you can create any song for any table your child needs to learn.....You can even create poems, as our Fourth Grade Teacher did....probably the "hard-parts" will suffice...ie. 7's, 8's, 9's, teach the 8's as doubles of 4's.