From the Irish Rail Website:

Bicycles are permitted on Commuter and DART services between 10:00 and 15:30 and after 19:00 Monday to Friday and all day Saturday and Sunday. Customers are asked to stay with their bicycles in the vestibules at all times and ensure they do not allow their bicycles to become a nuisance to other passengers. The carriage of bicycles on Commuter and Dart services is at the discretion of station staff. At certain times (e.g. major sporting fixtures /concerts), it may not be possible to permit carriage of bicycles on Commuter and DART services. Bicycles that are folded and covered can be carried on all Commuter and Dart services with no time restrictions.

If you are travelling with your bicycle, please note the following:

• Customers should walk with their bicycles when they are in the station. It is not permitted to cycle in stations or on platforms
• Customers should use ramps and lifts rather than stairs within stations to gain access to platforms
• Customers should stay with their bicycles onboard trains
• Unaccompanied children cannot bring bicycles onto trains
• No motorised bicycles are allowed on trains
• No bicycles with attached trailers are allowed on trains
• Always use available bicycle storage spaces provided
• Never obstruct exits or passageways