How can a bead on a car tire that won't seat on the rim be made to seat?

It's possible the rim itself may be rusted. OR it could be dirty.

Take the tire and rim to a tire shop. Les Schwab does a lot of stuff for free. They can unmount the tire, wire brush the seat and reinstall the tire. That SHOULD rectify the problem.

I remember many years ago my father had an issue similar - but so long ago I'm not exactly sure of the problem - so he took some wheel bearing grease and greased the bead then re-inflated the tire. I don't remember him having any trouble after that. But I was probably younger than 12 years old. Not likely to have paid much attention after that.

I learned a lot of things from my parents. Would have been nice to be able to show them all the things I've accomplished.

Since I don't have a clue who you are or how smart you are lets start with this. Are you trying to change your own tire or do you just have a leak around the tire bead to rim? If the rim is leaking you need to have the tire removed, the rim wire brushed or sanded to remove the pitting and corrosion, and then a bead sealer brushed on before mounting and balancing the tire. I don't even know if you have the correct diameter tire for the rim so if you're some how trying to mount a tire yourself good frickin luck!