Contribution Detail Report- "contact name suffix" isn't showing up as one of the possible report criteria
Allison, you're correct, neither prefix nor suffix is available (surprising) 
Assuming that coding isn't an option.  There are several ways to can export the contacts prefix/suffix.  For example You can...

Create report you want and include civicrm "contact ID"

If you can also create a contribution search that returns the same contacts, then you can export the search results and include the suffix field.

If you can't create a contribution search, then you can do an import "Update" and add a "tag" that will identify the contacts in your report (match on contact ID) You can then run a search and export the suffix.

If you'd like the report to include suffix, you can submit a request to the paid issue queue and the Core team will give you an estimate on what it will cost to add suffix.  Seems like a good way to contribute back a function that others would like as well.