Depends what you mean by hard, there’s not a lot of long climbs around but there are certainly some short, sharp ones.
For a short but rather nasty effort, Winwood Heath Road at the back of Clent/Romsley is worth a look. Sheepwalks Lane in Kinver is a good effort too.
Though not very pretty, there’s a lot of nasty little kicks heading from Halesowen or Old Hill up to Rowley Regis, Waterfall Lane being one, Gorsty Hill is not much fun either and, Coombe Hill is a very short, very ugly but very steep little kick too. I’m not a big fan of Mucklows Hill or Furnace Hill either but that’s more me than them being an overly nasty climbs.
The climb out of Arley, over the Severn Valley Railway is a bitch though I’m not sure it counts as West Midlands, in a similar area, there’s some nasty short stuff around Highley.
In fact, this has inspired me, time to get route planning and plot a nasty climbs route I think.