[Richard Crowley]

"RF" wrote ...
I have had a pair of Jensen speakers in my car for about 15 years but they
did not get very much activity in that time.

The diaphragms have 3 sections
- the inner one that looks like a low mound and is about 1" diameter.
- the middle one of about 3" diameter that the mound seems to sit on
- the outer one that is about 4" diameter maximum and is glued to the
middle one.

The inner two appear to be made from a thin brown cardboard and are in
excellent condition.

The outer one has a ridge in the middle that runs all the way around. It
appears to be made from a dark green paper and is disintegrating. This
green annulus is much worse on one speaker than the other.

Is there any way to repair these or are the speakers just throw-aways?

Valuable speakers can be "re-coned".
But you are likely correct, 15-year old ordinary
car speakers are likely throw-aways. It would cost
many times more than they are worth to repair them.
And much more to repair than to replace with a modern
speaker with likely better performance. You could try
it yourself if you have great patience and a lot of time on
your hands.