Hello Colyn - What you describe is probably a field collection, unless other information is in the donor file. Right now, the donation IS accessioned and I think, you are looking to catalog the items. There is a difference. You didn't mention where you are working as an intern, but whatever state you are in may have a state museum or university with archaeology staff who can prescribe the numbering method for that area. Here in NJ, there is a system for cataloging that notes numbers assigned to the site and then down to each object or unit of the dig.
the number denotes: state-county-site-unit-object. i.e 28-MO-12-32-0065.
The accession number may be used for numbering for an individual museum - i.e. 409-1978-32-0065 = site-donoryear-unit-object.
Hope some of this helps.
Good luck
Cheryl Stoeber-Goff, Museum Curator
Historic Services Division
Monmouth County Park System, 805 Newman Springs Road,Lincroft, NJ 07738
Phone: 732-975-9747 Fax: 732-975-9748