Available records in the U.S. vary from state to state, but even then I don't think you will find too many vital records that recent anywhere. Some exceptions, but very few.
Newspapers.com might have information on some families, especially if they lived in a small town with a local paper. There might be announcements of births and marriages, or human interest stories.
There are more recent censuses in the US than in the UK. 1930, 1940, and 1950. That might be a place to start, even if it would be for the generation before the people you are looking for. It would give you some idea of where the family was living. They might still be living there, esp. if they are there in 1950. People were still moving around a lot in the 30s and 40s, but things settled down after WWII. Unless it is a black family, then expect some of them to move north after the war for jobs and better conditions. Also California was still a big draw. Also, people when retiring often move south or southwest, Florida, Arizona, etc. Trend now is to the upper south, Tennessee through to the Carolinas and Virginia.
