The Prowlarr team does not offer an official Docker image. However, a number of third parties have created and maintain their own.
For a more detailed explanation of docker and suggested practices, see The Best Docker Setup and Docker Guide wiki article.
Synology Users can see TRaSH's Synology Docker Guide
Portainer should be avoided for setting up docker containers
See this Docker Guide and TRaSH's Docker Tutorial instead for how to setup Docker Compose.
To install and use these Docker images, you will need to keep the above in mind while following their documentation. There are many ways to manage Docker images and containers too, so installation and maintenance of them will depend on the route you choose.