This appears to be a corruption of a baby-talk form of address used in the 'Friends' episode called 'The One with the Baby on the Bus' (Season 2, Episode 6).
The show starts with "MONICA: Who da wenny-Benny boy? You the Wenny-wenny-Benny-Benny boy, yes. Don't cry. Don't cry. Why is he still crying?"
She is addressing Ben, the infant son of her brother Ross, who is about to have a big day.
http://www.twiztv.com/cgi-bin/transcript.cgi?episode=http://dmca.free.fr/scripts/friends/season2/friends-206.htm
Plot summary of the episode:
"Ben always cries when he's near Monica. Ross has an allergic reaction to Monica's Kiwi Lime Pie; his tongue swells up and he has to go to the hospital. Chandler and Joey take care of Ben for the day, but accidentally leave him on a city bus while meeting women. They retrieve him from Human Services, but are a little unsure whether they've got the right baby. Phoebe is displaced when Terry, the manager of Central Perk, hires Stephanie, a professional singer, to play at the coffee house. Rachel arranges for Phoebe to play after Stephanie, but Phoebe feels slighted because, unlike Stephanie, she won't be getting paid. She becomes a street musician, outside Central Perk. "
http://www.friends-tv.org/epshort.html#206
It's meaningless baby-talk - using a baby's name in association with nonsensical rhyming syllables. It means nothing, and is just a silly way of referring to him. It seems to have been adopted on a number of internet sites as a kind of fond way of referring to someone or something in a sickeningly sweet way. Similar to 'my huggy-buggy' and otehr such sayings.
