Coming from the east, your best shot is the
Coleshill Park and Ride.
Although trains every 30 minutes isn't exactly frequent.
Otherwise you can park at Birmingham International station (just by the airport, but don't park in the airport car parks) and take the train in. These are much more frequent, but there is something where you have to get a token from railway ticket booth so that you can get out again.
Getting into the city centre from the east isn't too bad, as long as you miss the rush hour. Parking is a bit of a mess, as business rate laws and the credit crunch means that there are a large number of ex-businesses that are now car parks offering such deals as £2.50 for a whole day of parking, whereas the Bull Ring special car park will charge you that for the hour. And you will still have to walk.