pleasant hillock?
The second element is most likely to be the adjective binn: its primary meaning is ‘melodious’, but it also has a wider meaning, ‘pleasant, splendid’.

John O'Donovan thought that this was the place referred to as ‘tulach mhoain’ in the Annals of the Four Masters, and that that Irish form was a mistake for ‘tulach mhaoin’ (cf. 'Tulach Moain, i.e. Moan's hill, now called in Irish tulaigh mhaoin, and anglice Tullavin' in his edition, Annála Rioghachta Eireann, V, 1375 note e). In fact this spelling ‘tulach moain’ is a phonetic rendering of an entirely separate name, .i. Tulaigh Mhongáin (q.v.). See ‘As Cartlann na Logainmneacha: Tullyvin’, Dinnseanchas V, 20, and a note by de hÓir s.v. Tulach Mhoáin in ‘Annala As Breifne’, Breifne IV, 13 (1970), 86; see also de hÓir, ‘An t-athrú onga > ú i roinnt logainmneacha’, Dinnseanchas I, 8