All of the opiates work roughly the same way, though some are more constipating than others, and that's the "side effect" we're looking for. It appears that the constipating effect doesn't diminish over time like the pain relief does, so a constant dose generally does the trick. Some folks here use codeine with good success. I'd strongly suggest trying Lomotil first, mainly because it causes the smallest amount of mental fuzziness that opiates are known for (most long-term users say they don't get this effect). In addition, Lomotil is by far the easiest of the opiates to get, and your doctor won't get harrassed by anyone for prescribing it. In some places you can only get long-term opiates from pain management specialists, and they don't know a darn thing about J-pouches.
If you're on long-term opiates you'll develop tolerance to them, and you should expect them to work less well at usual doses if you need them for pain.
In my experience these medications are most valuable at bedtime, but I suppose if you slow the gut enough (even during the day) you might get better water absorption, and that might reduce toilet trips. Most folks on around-the-clock opiates seem somewhat unhappy with the results, but I might be reading too much into it, and they might be worse off without the meds.
I'd suggest reserving the word "diarrhea" for loose stools ***with urgency***. It is normal for a J-pouchers to have soft stools. If all you want to do is thicken your stools, soluble fiber (e.g. Metamucil, Konsyl, Benefiber, Citrucel) are vastly better choices than opiates.