Hello Terry
I tried to find out about inquests too.
I had sent for a death cert for 1839. At the time I was hoping to confirm the identity of the deceased from the name of the informant. I was disappointed to see that the cert was signed by the coroner. Someone advised me to look in local newspapers for more information.
The helpful staff at the Worcestershire Family History Centre advised me which newspapers were likely to cover the area where the event occurred. I checked newspapers for dates immediately after the death and found reports in 3 different newspapers. The reports covered witness testimonies given at the coroners inquest which was held at the local pub. One of the reports gave several witness names (family) and described the suicide in great detail!
It would probably be worth searching newspapers for the 2nd half of October for your inquest. Staff should probably be able to suggest which Birmingham newspapers to check. It only took me about 15 mins looking through microfilm to find my first report as any newspaper article is likely to be very soon after the event.
It's certainly worth a look! Hope you find something.
Angela