Fortunately, since cataract surgery with lens implants, I can see well enough without glasses to get around (not to drive, but close), so I need only closeup lenses for reading/sewing, and get along fine with the generic drugstore reading glasses. I got those (for reenactment use only) at McAllister, although the frames are a bit too big for my head and also a bit too big for the period.
Another possibility is to get reproduction frames and take them to your regular optician to have the lenses made and inserted. That's what I would have done if I needed a prescription lens. You'll certainly get better lenses that way, but not all opticians will do that.
Actually, bifocals (the kind with the line) were invented by Ben Franklin, so they should be fine. Trifocals were invented in 1827. Again, those would have the lines between so would be authentic. However, most soldiers in the CW would not have been old enough to need multifocal lenses! OK if you're an officer.
Contact lenses are the most commonly used solution for reenactments, or you could get glasses with lenses for distance vision only and a second pair for reading. Although you will notice the difference between progressive (no line) multifocals, nobody else will if the frames are authentic. However, the small frames that were in use at the period might limit the vision fields for multifocals.
Here is a thread from "The Authentic Campaigner" with ideas:
http://www.authentic-campaigner.com/forum/showthread.php?33869-Reproduction-Glasses