Your struts are probably worn out which will cause the suspension to bounce or oscillate. I have Gabriel struts in the front of my 98, and am very happy with them. The KYB struts are stiffer, you may want to try them.
https://www.rockauto.com/en/catalog/buick,1996,riviera,3.8l+v6+supercharged,1022038,suspension,strut,7584
The Monroe shocks (MA822) for the rear are excellent,
https://www.rockauto.com/en/catalog/buick,1996,riviera,3.8l+v6+supercharged,1022038,suspension,shock+absorber,7556
Addco sway bars are a huge improvement.
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98 Riviera SC3800 All stock except gutted air box.
1970 Buick GS455 Stage1, TSP built 470BBB, 602HP/589TQ
Best MPH, 116.06 MPH, Best ET, 11.54
https://www.youtube.com/watch?v=UHCda-t_Jls
https://www.youtube.com/watch?v=sfT2tEO4XcU