I suspect that the service may have been withdrawn.
There's no mention of it on the Drayton Manor Park website:
http://www.draytonmanor.co.uk/ParkGuide/Direct ions.aspx
The Traveline website gives the suggested routes as either a train from New Street to Tamworth, to pick up Arriva service 110 from there, or a train to Wilnecote, to connect with Elkin Travel service 766:
http://www.travelinemidlands.co.uk
However, both of those routes seem leave you with quite a long walk.
The list of all Arriva services from Birmingham is here:
http://tinyurl.com/arriva
There's no mention of a designated service to Drayton Manor Park.
You could try phoning Traveline (0871 200 22 33) but I suspect that they'll just refer to the same database that's available online. Arriva normally direct travel enquiries to Traveline but their customer comments line (0844 800 44 11) might have further information.
Alternatively, try the Drayton Manor Park information line on 0844 472 1950 or email them:
[email protected]
Chris