One way to go up is from Carlingford. Start at around J1839 1095 A up a path (not the adjacent track). Following the path makes for an easy ascent. It is also possible to start on the SW side for example at J1600010505 B. The top area has a curious double summit. The higher westerly summit has a cross on it, the lower northerly one overlooks Carlingford and has a low trig pillar. There is a ridge extending south from the top to another slightly lower peak as yet of unknown name.

A great reason to go to Barnavave is the view south which may include the distinctive triangular shapes of the Great and Little Sugarloaf in Wicklow (98km away) Linkback: https://mountainviews.ie/summit/1504/comment/18839/

A number of years ago the BBC ran an Irish language show called "Ar Scath na Sleibhte", which provided a bit of inspiration for me to take a visit up to Carlingford, or "Carlainn" as I was to learn the Gaelic name to be. There are some clips and photos from the series still carried on the bbc website here (clips may not play in ROI):

http://www.bbc.co.uk/programmes/p03fw143/p03fw10k

The series was mainly focused on the mountains of Ulster but included an episode on "na Sleibhte Chuailnge", the Cooley Mountains. This episode obviously resonated with me as I learned some of the mythology of Maeve's Gap, “Bearna Mheabha” being anglicised as Barnavave, the gap which is visible when descending south-east off Slieve Foye.

While I like the tales of a giant or even of Maeve’s army digging out the rocks – the “Tain Bo Cuailnge” epic sounds like a long read. A geologist will probably give a more scientific explanation of the gap arising from a fault line in the rock with granite between two humps of gabbro. More on the geology of the area can be found here: A geological field guide to Cooley, Gullion, Mourne and Slieve Croob by Sadhb Baxter.
http://louthheritage.ie/publications.shtml

Though my primary objective was Slieve Foye and Barnavave just provided a slight detour on the descent, I recall thinking (like others have commented) that of itself Barnavave would make a very fine family walk from Carlingford (but more than enough to break a sweat from sea level) given that it can be accessed on a pretty low gradient track. There are fine views across the Lough from the trig pillar top, even when cloud has obscured Slieve Foye. I met three generations of the same family that had ascended a less taxing route from the west, the youngest daubing initials on the cross, which strangely seems to be the done thing.

Back then to the view of the “Lough”. If the Irish called this stretch of water “Cuan Carlainn”, it was the Norsemen that added the “ford”. The reason is as obvious looking north-east from Barnavave as anywhere. You've a bird's eye view of a very fine fjord, at least in name if not textbook glaciated character! I suppose the vikings should know what's a fjord and what's not! Linkback: https://mountainviews.ie/summit/1504/comment/19844/

At times the route up hill from Carlingford may be too steep for some and for those who wish to visit the new cross on Barnavave the option is to ascend from the opposite side . From J1600010505 B you can gently follow the Tain Way up to the ridge which connects this hill and Slieve Foye, a few meters before the ridge bear right and if you visit the trig first you will be rewarded with fine views over Carlingford , a short walk thru the little wooden gate will take you up to the cross. Linkback: https://mountainviews.ie/summit/1504/comment/19628/