I'm not really very familiar with Scottish music--just 'Farewell to Taiwathie', really. (Which is very nice. Especially the Judy Collins version....)
If you don't have anyone singing WITH you, I think sad love songs are ok. I mean, everyone seems to love the theme for Titanic--hello, the ship sinks! Some really pretty Irish tunes are Siul Arun, White Orange and Green, Salley Gardens, Leaving of Liverpool, the Flower of Sweet Strabane, the Daughter of Daniel O'Connell, and the West Coast of Clare. Dun Do Shuil is absolutely gorgeous, but I dunno where you'd get the music. Mairi's Wedding and Star of the County Down are both stunning pieces, but are originally played fast. If fast pieces are fine, you could play a nice reel or two--also in Kim Robertson's book. There is, yes, tons of O'Carolan--and also other slow dance tunes, like slip jigs or set dances. Think, "The Butterfly", and the 'Blackbird' is nice, also.
Really, the music depends on what the bride was thinking of when she said 'Celtic'. There is Irish, Scottish (actually, try Kim Robertson's Celtic Harp Solos book...that has nice Scottish and everything else, too) and then 'modern' Celtic, like Celtic Woman, Clannad, Chieftans, Maura O'Connell, Riverdance and Enya. And, also, American Irish, like Danny Boy and Last Rose of Summer. And English Folk, which some people associate with Celtic (Scarborough Fair, All the Pretty Little Ponies).
If the bride likes Enya, you're good to go. Her pieces are very Irishy and cover a wide spectrum of musical difficulty and sound. If you want a more 'conservative' Celtic approach, you could try some Mel Bay Irish books. They're brilliant and I have two or three. What are you playing for the actual wedding bits? Like processional, etc? A recessional comes to mind--Mairi's Wedding would be perfect. And I would say 'the Butterfly' for the processional, personally.
OH! There are tons of Celtic songs that have been rearranged as hymns, which would be great for the service part (if there is one). "Morning Has Broken" and "Be Thou My Vision (Sloan)"; some hymn books have "Canticle of the Turning" which is really Star of the County Down. (This is if they have a service or whatever--but if they are getting married in a church, check the 'Tune Names" listing in the index of the hymnal. They will usually list some Scottish/Irish/English Folk pieces.)
I love Celtic music, and I am so jealous! I would love to play a Celtic wedding...best of luck!
~Siobhan
PS--There is always the score to Riverdance, if all else fails!