Dave, a chara!
There are two Irish words normally used for "cairn", they are "carn" and "carnán". I'd say "carn" is the more usual form so I'd recommend that.
"At the cairn" is "Ar an gcarn".
I'm not sure about "Cnoc Mór". Sometimes adjectives in placenames are also put into genitive which would give "Cnoic Mhóir". Sometimes is is not, "Cnoic Mór". I'd say the first usage is more common, as in "Ionad an Bhlascaoid Mhóir". The best thing to do would be to check with someone who knows the place.
The genitive of "anam" is "anama". "Cuid a hanama" is "part of her soul".
To say "to rest" is "do scíth a ligean".
I'm resting = Táim ag ligean mo scíth
I've never seen "do scíth a ligean" used in this way, and I'd suggest you doubble check it. The Irish verb quite strongly suggests that the rest is temporary. On the other hand, that is also a rather nice thought. Anyway, you have to have an "a" before scíth since the construction require us to say whose rest we are talking about. The following sounds most natural in Irish
"tá cuid a hanama ag ligean a scíth".
It implies that the soul will rise from the rest one day.
"ligeann cuid a hanama scíth"
This construction is not as natural as the first one. I've seen it sometimes, more often than not from learners. That is not to say that it isn't correct, though.
So to sum up, I've ended up with something like this:
"Ar an gcarn ar bharr Cnoic Mhóir, Inis Bó Finne, Contae na Gaillimhe, Éiri, tá cuid a hanama ag ligean a scíth. Bealtaine 2003"
Still that sounds like an English phrase turned into Irish (not surprisingly, that is what it is). If I were asked to say the English version in Irish, I'd say:
"Tá cuid a hanama ag ligean a scíth ar an gcarn ar bharr Cnoic Mhóir in Inis Bó Finne, Contae na Gaillimhe, Éire. Bealtaine 2003"
Or if you want to emphasize that it lies ON THE CAIRN
"Is ar an gcarn ar bharr Cnoic Mhóir in Inis Bó Finne, Contae na Gaillimhe, Éire, atá cuid a hanama ag ligean a scíth. Bealtaine 2003"
I hope this helps. If you go to the Irish speaking list for questions like this, Gaeilge-B, http://www.smo.uhi.ac.uk/liosta/gaeilge-b/
I'm sure you'll find more people who are willing to help you. My suggestions are those above, I hope this helps.
Slán go fóill,