I have a 67 Coronet with the push button door handles. I hate that door rattle and the only thing that rattles is the door thumb button.
So I bought new made in AMERICA exterior door handles. I took them out of package and shook them. They were silent! WHOOT!

Put them in, The linkage pulls the bell crank and holds open the plate that the thumb button pushes on.....


Even though its better! By a mile.. We can do better.

I took a vacuum fitting cap that you can buy as assorted set from most auto parts stores. I used the white one. I cut the vacuum fitting cap in half or more, like a making short condom for the tip of the push rod.

All thats needed.
Take off interior door panel
Pull bell crank down,
Have helper push/ hold door button
Push on the rubber tip from a vacuum cap onto the thumb button pushrod.