SQLite is a good option for a local database that you can ship with your application. It wont require the user to setup or install any extra dependencies. Its certainly not as full featured as a full on server, but it should be good enough for a local desktop app.
https://github.com/louischatriot/nedb (last release 4 years ago)
https://github.com/pubkey/rxdb (many features, observable queries)
https://github.com/pouchdb/pouchdb (many open issues)
https://github.com/techfort/LokiJS (only in-memory storage)
https://github.com/typicode/lowdb (good for simple, small datasets)