Here's my take on the first two verses.

I'm Irish police, preserving the peace,
I belong to the Broadway patrol.
Don't I look grand with a club in my hand,
Every day out for a stroll?

It's a darling dove at the window above.
My Dolly, won't you come here?
Oh Dolly, oh clover, I'll arrest you all over,
I belong to the Patrick O’ clan.