if by holiday visa you mean visitor (B-1) no, they can't apply through Buffalo they have to do it from their home country
If you were originally admitted to the U.S. for at least 1 year, then you can apply from the U.S. It has to be for a full year - it can't be a 6-month period that was extended, for instance.
If you were not admitted to the U.S. for at least 1 year, then you have to return to your home country to apply.
They should not have a problem getting the police certificate they dont check your immigration status as long as they dont have a "record". They can try their local U.S. Consulate or Embassy. They usually can provide that service for a fee.