Tire balance is difficult on a trailer because you really can not set camber / toe accurately on a trailer, when you have a tire that is causing vibration and this is dependent on the fact that you have determined that there was no movement / damage done to the axle alignment at blow out, that it is most likely the new tire - one of the easiest things you can do is re-align the tire on the rim, mark the tire rim location with tire chalk, rotate the tire to a different mounting position - for balance I use / toss in tire beads, they seem to work better as run out can change, the beads will change placement, they work very well on trailers...