We need more information to answer this question. (We call it context.) You are allowed to quote up to four lines of the song, and to tell us what the song was about.
I looked on the internet for lyrics with this title, but couldn't find them. I did find a song 'Matchbox' sang titled "Buzz Buzz a Diddle It". The lyrics are Here. Is this the one you are thinking of?
Here are some of the lyrics:
I tried to call my honey
What was the sound I had to hear?
(Buzz buzz a-diddle-it) In my ear?
(Buzz buzz a-diddle-it)
The singer goes on to complain that when he tries to telephone his sweetheart, he can't get through because her line is busy. He thinks its some other man talking to her.
I think buzz buzz a-diddle it is a line they made up to represent the sound of the busy signal. "Buzz buzz" is an ordinary way to represent sound. "a-diddle-it" are probably nonsense syllables that are added to it, as Nunty explains. However diddle by itself is a verb meaning 'to swindle'. It also has the slang meaning of 'to have sexual intercourse'. Perhaps they want us to associate it with this last meaning and understand it as an expression of disgust, or a way of saying "forget about it".
Thanks a lot, Nunty and Cagey!
And sorry, I got it wrong but you corrected me Cagey. The sentence is indeed 'Buzz Buzz A Diddle It'. I agree with you for the 'forget it' meaning for 'diddle'. I hadn't thought of that. It certainly seems to be what fits best.
I think Cagey is right about "buzz buzz" referring to a busy signal. However, I believe "a-diddle-it" refers to the specific sound a coin makes going through the innards of a payphone when you hit the coin return lever.
The original performing artist for Buzz Buzz A Diddle It was Freddy Cannon, though this was not one of his big hits. In the context of his time, it makes sense if you picture the song's protagonist repeatedly putting a dime into the payphone, getting a busy signal, hitting the coin return, and dialing again obsessively while imagining his girl is talking to some other guy.