There is at least one taxi with an electric lift with this company http://www.galwaytaxis.com/
Phone: 091- 561111. I spoke to him before and he said he could bring a mobility scooter on the taxi, but to ask for the taxi with the lift.
If it is a 3-wheeler scooter some of the ramps leading into some of the taxi's might not be totally suitable (if the ramps that are just a one big piece they are probaby ok, but the ones which are 2 sections (one for each side of a 4-wheeled wheelchair/scooter are not really suitable).
Another option might be the Galway Centrey for Independent Living. They have big vans with electric lifs, but you would need to book a bit in advance, 091- 773910.