The local would need to petition the General Secretary Treasurer of the IBT for a dues waiver. This would have to be a local-wide initiative and not just for one center (assuming there are multiple UPS facilities in your local's jurisdiction.) Depending on how many UPS members your local has and how your local's finances look, this could have serious financial ramifications. Quite frankly, the only way to get it done if the principal officers aren't interested is to pack the union hall with angry part-timers and bring it up every meeting, but that's much easier said than done.
The IBT constitution sets dues at 2.5x the base hourly rate of pay for members, with the rate being 2x for members making less than $11/hr. Some locals charge as high as 3x the hourly rate. One thing my local does in the RTW south is waive the initiation fee for PT new hires, which can be as much as $180-$200 in the closed shop states. If your local charges initiation fees, I would suggest focusing on convincing the executive board to waive these instead.
Although I disagree with Fred Z (president of Local 89) on many things, this is one of the good things he does -- getting reduced dues for his PT members who primarily work at the Louisville, KY UPS Worldport as they actually have a smaller guarantee than most PT'ers in the rest of the country.
See:
http://www.teamsters89.com/hall/June 7, 2012 Request to hall.pdf