Is it acceptable to miss out joining words (e.g. who, which)?

Solution 1:

According to Wikipedia, the modern version of the song is:

"There Was a Farmer Who Had a Dog".

• It is an English language children's song of obscure origin. In most modern forms, the song involves spelling the name of a dog (Bingo) , and with increasing letters replaced with handclaps on each repetition.

"There was a farmer had a dog" (the original and still used title), isn't proper grammar, but it isn't meant to be. It's meant to follow the meter of the music.

This is also an old-fashioned structure you'll hear or see in old books, and it was often the way people of the lower classes spoke. For example, in the Shakespeare play Henry IV, Prince Henry says, "there is a devil haunts thee in the likeness of an old fat man," notably missing the joining word between "devil" and "haunts."