A couple of problems - there's a lack of maps around that time, nothing decent until 1890ish and New Road may have been that at the time, just laid out and then renamed.
One clue may be that another address that seems to be on the same page as New Road is Regent's Park and there is a Regent's Park Road in Small Heath.
If you have access to the scans you could just flick next and previous to see if there are any other roads that are recognisable.