There are a couple of car-parks near the centre. The nearest is probably the Irish Life Car Park , which is accessibly from Lower Abbey Street. Another close one is Q-Park on Marlboro Street (listed under 'Q-Park Clerys' in Dublin). This is roughly 5 minutes walk from the centre.
On-street parking is available on James Joyce Street and there are usually spaces available in the evenings. This is free of charge after 7pm. As usual when parking anywhere in the city-centre, we'd advise you not to leave any valuables visible in your car, as this will encourage theft.
If you're cycling to the centre there are many places to lock your bike on Talbot Street. There are also posts you can lock your bike to on James Joyce Street, but, unfortunately, bikes have been stolen from here, so we'd recommend locking your bike on Talbot Street.