Steve:
"I would like the various suppliers to be the vendor, but for the PO to use the co-op's contact info."
That would be my preference also. Unfortunately there is no good way to do this in Adagio. We need to be able to default the Bill to/Ship to or Pickup Code to the vendor profile.
Depending upon what you are already using them for set up either a Bill-to or Pickup code to include the co-op details.
The best option is to either manually add one of these codes to each PO or default one in the template and remember to take it out on any PO not for the co-op.