There?s a Daniel Dungan listed in Lismonaghan in 1858 in Griffiths Valuation. I suspect that may be your Daniel, with his name being mangled slightly, because he was listed as farming the plot (plot 9) jointly with Michael McIlhenny, the same as in the tithes.
There?s a Donegan family there in 1901 (which could be another variation of the name Dungan). Rag dealers rather than farmers so can?t be sure it?s the same family.
Can?t find a death for Daniel. Perhaps he died between 1858 and 1864 when statutory death registration started. He doesn't appear to have left a will, or at least not one that was probated.