This is a cutesy term meant to make pit bulls seem cuddly.  It is the verbal equivalent of dressing a pit bull in a tutu. The Urban Dictionary offers the following definitions:

A slang term for Pit Bull; makes the dog sound more friendly and cute
“I need to go feed a hungry pibble”
A term of endearment used when referring to American Pit Bull Terriers, American Staffordshire Terriers, Staffordshire Bull Terriers, or any one of the three mixed with any other breed of dog.
“My dog is an adopted Pibble.”
the more refined and less aggressive form of pit bull. a kinder, gentler term that better reflects the true nature of these great friends.
“i cant get this damn evil pibble to stop snuggling with me. GOSH!”

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