You'd really have to talk to your doc.
There are two types- the Mirena IUD contains progesterone, one of the hormones found in bcp's. That tends to lessen cramps and lighten periods, and may help you out.
The other kind is the paraguard- which is copper and contains no hormones. That may worsen cramps but has less hormonal side effects.
So it seems like the mirena may help you the most- but it's always something you will want to talk to your doc about.