The easiest way in terms of fewest changes etc. is probably to get the bus in from Blanchardstown - if they haven't changed then they'll stop on Parnell Square where you should be able to change onto a number 10 which will bring you out to Donnybrook. Actually I think all of the 46 buses now start on Parnell Square and any of those will bring you to Donnybrook (but some may be minimum fare so check that they do stop in Donnybrook).
I know there are some buses early in the morning which don't stop in town but continue out to Morehampton Road or UCD e.g. the 66 from Leixlip, there are a few 66X in the mornings that do this. Check with Dublin Bus if any Blachardstown buses to this too.
If you were to get the DART either Lansdowne Road or the next stop would suit depending on which end of Donnybrook you need to get to. But it's a good half-hour walk.