I got a remote off of eBay for my Pioneer CD changer and after I put batteries in it and confirmed that it worked properly, I pointed it at the Magnavox just for fun and would you believe it? The thing operates the Magnavox as well! The only button that didn't work was the power button. I would never have thought that would have worked but in looking on eBay, the Pioneer and Magnavox units from the late '80s looked a lot alike. Makes me wonder if Pioneer made CD changers for Magnavox or vice versa. Either way, I'll now be looking for another Pioneer remote of the same type to use with the Magnavox.
UPDATE: On closer examination of the Magnavox, I realized the reason the remote won't turn it off and on is because the player is not designed to do that remotely. It has a power switch with two physical positions for off and on. Still, I'm quite pleased with this discovery.