It was more along the lines of a website powered by an online database, rather than anything to do with a locally installable client. The webhost provider did not support neo4j, the project was a hobby project so we did not want to buy a professional virtual server, and commercial neo4j-online solutions were prohibitive for what we wanted to do.

I haven't used docker much, but I don't know how it could help here (unless you misunderstood and were referring to locally installable software).