Grace's Guide is the leading source of historical information on industry and manufacturing in Britain. This web publication contains 149,270 pages of information and 234,239 images on early companies, their products and the people who designed and built them.
1860: George's Dock, North Wall. Balance rolling bridge constructed in 1860 by Turner and Gibson of Hammersmith Foundry, Dublin. Designed and patented by Michael Kenny, foreman at the Oxmantown Foundry. Crossed a waterway 47 ft wide.  
1879: Butt Bridge crossed the Liffey near Beresford Place. Built 1879. Designed by by Bindon Blood Stoney; General contractor J Doherty; ironwork supplied by Skerne Ironworks Co . Drawing and brief description here. The design allowed for replacement of the swinging section by a masonry arch. The bridge was decommissioned in 1888. New masonry arch span built, and opened in 1932 .
1912: Scherzer Bridges, North Wall Quay. Twin bascule bridges 
A remarkable bascule bridge designed in 1878 by Bindon Blood Stoney to carry a short branch of the Midland Great Western railway of Ireland across the Royal Canal, immediately below Newcomen bridge at the very oblique angle of 25°. Although the canal is only 15 feet wide, the bridge was 40 feet long on the skew. The rails were 2 to 3 feet above the canal's water level, and to allow passage of boats, the bridge was lifted 8 to 13 feet (according to the height of the deck load) so as to permit the boat to pass. This bridge was replaced in recent times by a 'four poster' skew lift bridge constructed by Somers Railway Engineering. This bridge remains in use.
The Spencer Bridge or Sheriff Street Bridge carrying Sheriff Street over Spencer Dock was described as a swivel bridge when opened in 1873. It was designed by James Price, and a wooden buoy 10ft (19 ft?) diameter and 10ft deep supported 95% of the weight of the movable span. It could be opened in about 3 minutes . Replaced in 1941 by a lifting bridge (drawbridge). Recent photos here.