These rail times should meet your requirements:
OUTBOUND:
Depart Knaresborough 1335
Arrive Leeds 1421
Depart Leeds 1510
Arrive Coventry 1823
OR:
Depart Knaresborough 1605
Arrive Leeds 1651
Depart Leeds 1710
Arrive Coventry 2023
RETURN:
Depart Coventry 1726
Arrive Birmingham New Street 1747
Depart Birmingham New Street 1803
Arrive Leeds 2102
Depart Leeds 2116
Arrive Knaresborough 2202
The return fare is �43.30. (Unfotunately, there are no pre-booked discount fares available).
Rail timetables are here:
http://www.nationalrail.co.uk/
When you get to Coventry rail station, walk to Warwick Road (2 minutes). If you caught the earlier trains, there's a service 12 bus at 1847 which gets to the Uni' (Arts Centre) at 1908. If you travelled later, the bus service you need is U1. It departs at 2054 and arrives at the Arts Centre at 2110.
On Sunday, there's a service 12 bus at 1640 from the Arts Centre. It gets to Warwick Road at 1657.
Bus information was taken from here:
http://www.travelinemidlands.co.uk/
The initial source for this information was this:
http://www2.warwick.ac.uk/about/visiting/direc tions/train/
Chris