we paid 5 pounds last September in the car park that's past Albert Dock by the Echo Arena. Probably could have parked closer, but it was a 10-minute walk, so no big deal. Price is still 5 pounds for up to 5 hours and 8 pounds for up to 9 hours.
Nothing was going on that day at the arena so easy in and out and paid by debit card. There's a car park very near the office as well:
http://www.thecapitalcarpark.com/. For 5 hours, you are looking at 7.50, but go over and it jumps to 10.50.
The Liverpool 1 car park is 9.00 for up to 4 hours, so maybe I would walk down to the Arena area.