Well doubt you have 31-10.50 any things on a Suoerduty, but icbw. Those are typically 15" rim light duty tires.
But assuming you have 80psi tires rates in the 3000lb or more range which you likely do, just up the rear pressure until it's not squishy unless it's not the tires and it's the suspension.
Normal range for the front of a 3/4 ton truck is 50-70psi depending on whether it's a diesel and what size tires. Pizza cutters and diesel = higher psi. Big tires and gasser = lower psi.
On the rear, you can run 30-40psi empty depending on tire size and go up from there for load applied to the truck bed or hitch.