No, not the Belmullet Canal, nor the Cong Canal. James McParlan MD, in his Statistical Survey of the County of Mayo, with observations on the means of improvement; drawn up in the year 1801, for the consideration, and under the direction of The Dublin Society [printed by Graisberry and Campbell, Dublin in 1802 and available here courtesy of Messrs Google], after mentioning some lakes and navigable rivers, said:
Those are the only navigations or navigable rivers in this county, except the Marquis of Sligo‘s canal, which winds for several miles through his demesne; it serves for conveying sea and other manures to different parts of the demesne, for conveying among the fields turnips and green feeding, and for several purposes.
I have looked on the OSI 6″ maps [~1840] at the Browne estates listed on the Landed Estates Database, but I have found no sign of the canals. I didn’t know where to look, and the good marquis owned a lot of land, so I may have missed something; furthermore almost forty years elapsed between McParlan’s work and the publication of the OSI maps and the canals may have fallen out of use in that period. If anyone knows where they were, and whether any trace remains, I would be grateful for information.