The expression "bada bing" and often accompanied by "bada boom" is used when something was very easily accomplished or as an euphemism of the nastier bits of something (like in the Godfather). A quick look on Wiktionary and Urban Dictionary confirms this.
It seems onomatopoetic because of bing and boom, but where does the "bada" come from? The whole phrase seems to be a recent invention according to this Ngram, starting in the late 1980's (surprising it was not sooner with the popularity of the aforementioned Godfather being released in 1972) peaking in the 2000's (possibly in part to the popularity of The Soprano's). The phrase does seem to go hand in hand with Mafioso culture as well.
So, where does this phrase come from and when did it take on its current meaning?