Just remember that capacitors can HOLD CHARGE for a long time after the amp is unplugged, and in some cases the discharge of juice into your body can KILL YOU.
If you don't know much about electricity, you're better off having an amp tech do it for you.
Well, if they’re that old, surely the filter caps (electrolytic) have been replaced at least once, that is, if the amps still work at all! The dielectric in electrolytics dries up over time rendering the cap incapable of holding a charge and 50 years is way too long even for the much better caps being made today. I’m not familiar with the Magnatones. Some old amps had these things that look like small, skinny aluminum cans sticking out of them that had the filter caps built-into them. Anyway, if you don’t think they’ve been replaced in a while then replacing them sure wouldn’t hurt. And like wrenhunter said, if you don’t know what you’re doing, take it to a pro – the voltages stored on the caps can be lethal!
However, the problem you’re describing sounds like either a defective by-pass cap (had a ’68 Twin Reverb with this problem, once) or a carbon resister breaking down. You just have to replace them until you find the one that’s defective. If it were me, I’d replace all the by-pass caps anyway.
I've got an old musicman that acted up a couple years ago. Had a professional tech replace all the caps. Cost me about $135. Best $135 I've spent. This amp sounds great now. He also had the equipment to measure noise, power output, tools I didn't have. I know my amp is in overall good working order.
I'd take it in to a good shop. Ask around before you select a shop, they aren't all the same.
One obvious thing you might listen for, if the amps work at all in their current state, is the presence of a "farty" sound on the low-E-string notes, a cap job would fix that.
And yes, check around for a competent amp tech! And ask for the old parts back.