Hi Suzie,
The family history records are currently in the Liverpool Museum on the 2nd floor till the new records office opens some time next month. There are BMD lists there, though you'd have to order a certificate from the records office, which you can do on line or by phone. If there was a coroner's report it may well be reported in the local press in the Coroner's Inquests columns. I've just been there today looking up a report of an accidental death in 1870 and found two reports which gave a great deal of background information not available anywhere else. There are several daily and weekly papers in the family history section and you can either book a microfilm reader ahead or just take a chance and turn up, which is what I've been doing and so far got lucky. Good luck.
Angie