Sally wants a new bicycle, but her mother and father will not buy her one. correct punctuation
The comma is correctly used in that sentence.
http://grammar.ccc.commnet.edu/grammar/commas.htm
See #2.
yes
"Sally wants a new bicycle, but her mother and father will not buy her one."
Sally wants a new bicycle, but her mother and father will not buy her one.
To correctly punctuate the sentence, you would add a period at the end:
"Sally wants a new bicycle, but her mother and father will not buy her one."