Hi blodwyn,
Just visiting from the Wales board, having read Celias posting.
I've just tried to look at the IGI, but the site is down at the moment.
Have you searched there for the births/baptisms of Alfred, Sarah and Mary Ann? The chances are you could strike lucky, as Ashford is not a typical Welsh name at all. Do you have any other infomation at all? Maybe from the FreeBMD site regarding the births of Alfred, Sarah and Mary Ann?
If the family emigrated to the US from Wales, this would narrow down the number of possible ships. Have you found their immigration details? As you know the date they arrived in the US, this might be a possibility worth investigating.
All the best
D ap D