Heroku was the leader for some time until they discontinued their free tier.
Here are some current options for backend services that you can use for free.
Codehooks
The blurb: Codehooks is a "no-setup", quick and simple to use backend service, bundling essential features like serverless JavaScript code, a NoSQL database, a Key-Value store, scheduled jobs, queue workers and more.
Comes with a CLI tool and a JS library. Integrations with Alpine JS and how to get Chat GPT to write the code for you.
CSV2API
The blurb: CSV2API is a tiny project that helps noobs to integrate a Database with beginner knowledge.
Supports querying but does not mention POST requests.
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The blurb: With our sponsor Mockend and a simple GitHub repo, you can have your own fake online REST server in seconds.
designed for testing though allows posts so could maybe used for something else?
Gitrows
The blurb: GitRows makes it easy to use and store data in GitHub and GitLab repos and deliver them with a powerful API..
GitRows implements a full Create, Read, Update and Delete interface to .json or .csv files in your private or any public repository.
App Backend
The blurb: A simple backend for your static website to make dynamic.
Formally Table Backend. Comes with analytics, CDN and a caching layer. Limited documentation. No mention of posts.
Railway
The blurb: Railway is the cloud for building, shipping, and monitoring applications. No Platform Engineer required.
Lots of templates for one click deploys such as NodeJS, HTTP NodeJs, Umami, Postgress, SQLite, Express and many, many more.
Render
The blurb:
spins down after 15 mins of inactivity. Takes 30s to spin back up when a request comes in.
Cyclic
The blurb: Build and run modern cloud-native serverless applications without piling on to the full stack.
Fly.io
The blurb: Launch Apps Near Users. Fly.io transforms containers into micro-VMs that run on our hardware in 30+ regions on six continents.*
Planetscale
The blurb: PlanetScale is a MySQL-compatible serverless database that brings you scale, performance, and reliability — without sacrificing developer experience. With PlanetScale, you get the power of horizontal sharding, non-blocking schema changes, and many more powerful database features without the pain of implementing them.
CockroachDB
The blurb: Run mission-critical apps on CockroachDB — the cloud-native, distributed SQL database designed for high availability, effortless scale, and control over data placement.
Supabase
The blurb: Supabase is an open source Firebase alternative. Start your project with a Postgres database, Authentication, instant APIs, Edge Functions, Realtime subscriptions, Storage, and Vector embeddings.
Traversy NodeJS REST API without framework
The blurb: Let's create a REST API using Node.js only, without Express
Harder than a setup using Express JS.