The Caribbean Coast is much like other parts of Nicaragua: it can be dangerous, but you should be fine if you're careful. The region is relatively remote, and armed gangs of highwaymen have been known to rob the unwary, but such occurrences are uncommon. Remember, the Caribbean coast is the poorest part of a very poor country, and leaving valuables around may prove irresistible to locals.
One important safety factor often overlooked has to do with the weather: hurricanes between July and November can hit the region hard, wiping out whole towns and roads. Be sure to keep a close eye on the weather reports and skip town if a storm appears to be on the way.