Bob,
I've seen that
Sony D-E351 has a resume function, there's a couple on Amazon.
Really good review of a chap using the resume play function of another Sony Discman for listening to Audiobooks:
https://www.youtube.com/watch?v=O-GaptilMMg (you've probably seen it in your search for the Resume play feature - that's how I found it anyhow)
The model that the chap is using in the video, I think is the
D-E406CKAN. If you search for that part number on Ebay you will see at the very moment there are three or four there for between £15 and £20. Another is a
D-242CK or
D-E400AN or
D-180AN or
D-EJ615 (there are plenty more it looks like). Incidentally there are over 350 Sony Portable CD players on there too, and I'm preyty sure if you looked up the specs of some of them they may well have the resume feature you are looking for.
The most recent Sony Portable CD player (from what I can see) is the Sony
D-EJ021 - which also has a resume function. The model looks like the buttons could be a little small though compared to the older models.
You may find that your local "Cash Converters" (and similar type of stores) may have these older portable CD players in stock which you will be able to look at. Your nearest one is in Salisbury I reckon (going off your profile description) their website for looking at items is
http://webshop.salisbury.cashconverters.co.uk/ (I'm not sure if that shows all their stock or not, but it's a start).
Trystan