Well, it's an earlier era, but if you like Swing Kids, than you will love Newsies.
I know there are tons more than the ones already suggested, but I am drawing a blank, I found some of thee online, some i know are kids safe, others n so sure, you can check on imdb.com.
Would Truman Show or The Majesty count? I can't remember those eras exactly. Wild Hearts Cant Be Broken, The Black Beauty, It's a Wonderful Life, A Walk in the Clouds, October Sky (good one for the kids), Pleasantville, The Other Side of Heaven, West Side Story, Grease, Hairspray, Stand By Me, My Girl (good for the kids), Paper Moon, Bringing Up Baby, The Lady Eve, The Palm Beach Story, A Night At The Opera, His Girl Friday, Ball of Fire, My Man Godfrey, Chariots of Fire
The Philadelphia Story
Here are some, but not sure of the kid-safe factor on all:
http://answers.yahoo.com/question/index?qid=2007123123151...
Do you have Netflix? If you choose a movie, they usually will suggest movies that are similar and can find lots of good ones that way.