As a character created in a medium with sound, Harley Quinn's voice has always been easy to fit into the concept of how we read her in the comics. There is not much more to this post than to have a look (or listen) to how she has been portrayed with her think Brooklyn accent (some of these links might need to be followed to youtube)
Batman: The Animated Series (starts at 0:08)
The original and so could be considered the best.
Not as strong an accent
Birds of Prey (starts at 0:07)
Batman The New Animated Series
Batman: Brace and the Bold (starts at 0:10)
Not really an accent at all, just a different sounding voice.
And a couple of video games ...
Batman: Arkham Asylum (starts at 0:22)
Very toned down accent but still there a little
Batman: Arkham City