Once you start looking, you can usually find old-looking fabric. Remember, you are not trying to convice anyone that these quilts are perfect and you are probably not goiing to try to pass them as antiques. I imagine you want to make them usable or even 'display-able'. Museums often display pieces of sculpture or pottery with obviously new material added so you can see what you are looking at.
I have had good luck appliquing fabric over the old. That way, you not destroy or remove what is old, just repaired so it will not destruct any more.
A previous person suggested tulle -- I use grey or at leasr not bright white over areas that are obviously weak, with maybe a few tiny holes. Again, not destroying, not making new, just pringing it to a place where use will not destroy.
It will be a labor of love.