I have an old character phone which was hardwired to the jack on the wall. How can I rewire with a new four wire connection which plugs into the wall jack?

You need to gt a cord like this, or 1 from a scrap defective phone, they are everywhere, even cordless have good cords.
They usually outlast the phone. Just use the red and green for line one, yellow and black is line 2 and can be cut if no dead terminals exist.