There are a number of long-distance walking and cycling trails through the beautiful drumlin landscape of County Monaghan, including the ‘Ulster Canal Cycling Trail’ which is a 77km on-road cycling trail which roughly follows the route of the Ulster Canal. 
Sport Ireland have a fantastic website called IrishTrails.ie with a handy app that provides reviews, ratings and maps for walking and cycling trails across the Republic of Ireland and gives links for cycling websites in Northern Ireland.
Ulster Canal Greenway 