Theres also the Royal Irish Academy and the Conservatory of Music in the DIT.
Both are great schools though I personally prefer DIT. Both offer a lot to take part in outside of classes such as ensembles and big bands etc if that tickles your fancy. Both mainly teach the classical side of instruments but both offer excelllent part time, once a week tuition with varying contact time. (min 30 mins, max 1 hour per lesson I think it is). I think the price is roughly about €500 per instrument for 30 mins for the year, though for an extra €100 you can also do a part time music theory class. I think this can vary though depending on instrument...... best bet is to suss it out online.
Newpark is good too, though from what I've heard it can be a little bit pretentious and "stuck" with its methods. I know a few past pupils from the place and while most of them loved it, most of them pretty much said that it isn't broad enough genre speaking. This is only what some people have told me, so don't shoot the messenger on this one. Its pretty much a jazz ONLY school so if jazz isnt your thing then you might be better off somewhere else. Don't get me wrong, if you want to study jazz you probably couldnt find a better program anywhere else in the country. Newpark is also more expensive in comparison to a lot of other schools, though it is excellent at what it aims to achieve. I dont know if it has a part time programme....check its website for details.
Waltons is a mix bag from what I've heard. Can be great depending on your instrument, although I've heard that the singing tuition there is pretty good.
There is also the Music Artistic Development (MAD) at Music Maker in town and the Xmusic academy out in Xmusic. Both are very new so its hard to judge if they are any good. The Xmusic academy boasts a list of experienced teachers, but as I'm sure you're aware, an experienced player does not necessarily make a good teacher and vice versa. The location can be a bit out of the way for some people, it really depends on your own circumstances.
As for MAD, well a recent google search for Music Maker informs me that their new website is coming soon...
However, OP, at this time if year your chances of getting in to any music school probably wont be too great as usually by this time of year the places are already taken up. You could apply again when they are accepting applications (usually in the new year) for the 2011 - 2012 season. Your best bet would be to ring / check up online / call into the schools and see what the situation is.
Oh and finally, as Im sure you're aware, you only get out of tuition what you put in, so if you cannot commit the time to practice (at least about 30 mins per day they recommend) for whatever reason, then maybe your best bet would be to get private tuition on your own time...
Hope this helps!