I have some experience with Lionel rolling stock in that I searched ebay and any place that I could find for anything with food and beverage industry advertising. Three hoppers I purchased had the trucks attached with rivets. Some of my box and reefer cars have riveted trucks. Yet some of them are installed with trucks attached with screws. Falconservice mentioned the danger of drilling out a rivet causing excess heat and melting the truck.
In the case of the three hoppers, I didn't like the overt way the cars swayed from side to side. It was due to excess gap between the truck and the body due to the rivets. I know train cars teeter from side to side as they follow along on the tracks, but these cars looked like fans at a rock concert with lighters swaying to the final song. So I fixed the problem.
I used "my method" mechanics to do this. I didn't have any rivets so I looked at the hole the rivet exited. I used needle nosed pliers to pinch the bottom of the rivet until it was narled to the point of falling out. Once I saw the hole I realized that if I could find the correct size, I could use those fender clips that hold a car fender to the body. They are plastic, have a flat round top with a triangular underbelly that when slid through a hole, if long enough, they slide through then fan out on the other side of the hole remaining locked in place. I think the Nissan clips were the right length and size. To my amazement, the idea worked. The trucks still turn unimpeded left and right, the cars have no problem following a line of other cars or navigating a switch pattern, and, most of all, the body of the hoppers still jiggle side to side like a real train car, but they don't look like windshield wipers. So this may be a possible solution if, like me, you aren't familiar with rivets and how to install them.
Another fix I tried and was astonished to find that worked. I have a Jolly Green Giant reefer that needed new trucks. Old ones were rusted. I bought some nice new Lionel trucks that attached with screws. Guess what. Didn't see that they were on with rivets. So, out came the "my method" tool box. I found the right size screw, longer than the ones normally used, then used a washer to cover the rivet hole that had a small enough hole to keep the head of the screw from falling through. The Nissan method, I just coined, wouldn't work here. The holes on the trucks were too small. The hole on the flat part of the reefer was big enough, but not the hole on the truck.
Just thought you might like to know.