Just leave the basic definition of the site  column set to optional. Then go to
the content  type where you want it to be required  and edit the column  from
inside the content type  to set it to be required. It will be required for that
content type and not the other.

I had the same issue. There was an instance where I could not use the
Title column  nor could I edit the name and use that because I needed
another column type. Since you cannot delete the Title column I
researched hiding the Title column and found two almost identical
posts. The key is to use Content Types. Once enabled you can hide the
Title column, disable the required  data entry for that column and
remove it from all views that would see the column.