Can't add much to the above but I was also going to suggest getting the tram in to Shudehill and then you aren't racking up expensive parking charges, especially if the coach is late. Plenty of places nearby you can get a coffee or bite to eat.
Do be warned though there are currently works going on on a second city tram line so services via Victoria Station (stop right before/after Shudehill depending on which direction you come from) so keep an eye out for that and they seem to love doing work on the network on the weekends and taking tram lines off, especially on a Sunday!
I wouldn't recommend on street parking if you don't know the area - we have militant traffic wardens in force! There are some cheaper car parks though some of them aren't legit (especially pop ups when big shows and football are on). There are a few just out of town but depends on how much of a walk you want and whether you can find your way about.
There is a hopper bus though which is free which may help get you to further out ones. There is the number 3 bus which would get you from the old BBC site which is now a big car park to Shudehill, could well be cheaper!
http://www.tfgm.com/buses/Pages/metroshuttle.aspx
Where is it you are coming in from and what day/time of day? Plenty of car parks, as said, and one right on the interchange.
Shudehill is basically a bus terminus, enclosed long oblong shape with buses coming in and round and out in a loop around it.
Another thought is if they do a stop off just before the city centre which may be easier to get collected from.