It might help if you gave a little more detail on the type of Engineering you wish to study? Civil, Mechanical etc.
Also, do you wish to do it by distance learning?
If not, it would be beneficial to give what area you're in (no point in giving a list of Dublin colleges if you're based in Kerry).
There are lots of courses available both part time and distance learning (up to you how much you take on in a given quarter [up to certain limits]) so plenty of choice available.
I would like to study Civil Engineering. I am based in Galway. I have not been able to find any distance learning courses except for Civil Engineering (Distance Learning) MSc / Diploma / Certificate at Heriot-Watt University, Edinburgh. I have not come across any part time courses in Galway, Athlone, Limerick or Sligo. I know there is a 1.5 day per week course at DIT.