The Jewellery Quarter Research Trust has records of all people buried in the Warstone Lane and Key Hill cemereries (where names are known). You could search their database for any family names you might have. If your chap worked and lived around that area, then it might be that he was buried in either of those places. But, there were many common graves, where I think not all of the names of people in those graves are known.
www.jqrt.orgIf you find any of your people, then if you want copies of images of the original burial records they can be obtained for a fee, from the Birmingham & Midland Society for Genealogy & Heraldry shop,
www.bmsgh-shop.org.uk/BIRM-CemeteriesAlso I believe that Handsworth Cemetery oversees those two, and Witton, possibly other cemeteries, so you could try them, I gather they're very helpful, though haven't needed to contact them myself.
If you use a search engine for Handsworth Cemetery, Birmingham, and also Witton Cemetery, Birmingham, and Birmingham Cemeteries, there are lots of options to choose from that will tell you more, and give their contact details.
Hope this helps
mogwood