One option is to fly to Corozal, cross the border, bus 5 hours to Cancun and fly Copa one-stop to Managua, with a change of planes in Panama City. Until recently, you could have skipped the bus entirely by flying Alma de Mexico from Chetumal to Cancun, but that service has been discontinued.
Not a great option, but you could also bus to Guatemala City via Flores on Linea Dorada and ADN (about 14 or 15 hours on a bus, not quite 24 hours) and then fly Copa nonstop to Managua. From GUA there also are one-stops on Mexicana and LACSA.
--Lan Sluder