Can't think of anything from the 50's. The first song that sprung to mind that opens with sirens is "Blockbuster" by The Sweet, released in the early 70's.
I am sorry I can't help. I was not born til 79. I do like the oldies music though. The only thing I can think of is the YMCA song. But that has a policeman and an Indian singing and dancing around that don't have fire sirens in it. You can always try calling your local music dept. Store. At some Hastings they have computers that you can call someone who works there and tell them some of the words in the song or some lyrics and they can usually pull up the song, singer or group, and or album with it. I would maybe try that also. Hopefully, someone here can help you out more though with this. Good luck.
I'm trying to think and The Night Chicago died comes to mind, do you remember any of the words at all?
Riot in cell block #9 1954 the robins later became the coasters