Retag and push to a local registry. Lots of options out there for setting one up.

Honestly, you already have the image locally if you've pulled it. You don't really need to run a registry unless you're dead set on it. You can also flatten and export containers for backup if you really want.

The vast majority of selfhosters probably don't but if you want its called a private repository

https://www.digitalocean.com/community/tutorials/how-to-set-up-a-private-docker-registry-on-ubuntu-20-04

Just use a sonatype nexus 3 image and proxy docker hub, etc. Then you pull images through it.

Sorry for the link dump - I just glanced over the content and it seems like this might help you:

https://www.warpbuild.com/blog/docker-mirror-setup

https://medium.com/@shaikrish27/deploying-a-docker-registry-mirror-as-a-container-59565ff92c48

https://blog.alexellis.io/how-to-configure-multiple-docker-registry-mirrors/

https://stackoverflow.com/a/41593925

At my job, we run goharbor.io and use its Replications feature to do just that.

For most of you suggesting hosting a repository - yes but,

Host forgejo. Just host the git mirror. It comes with a package repo out of the box. Then you have the source code and the docker images

I mean you have the current image cached on the local server when you use it.

I don't know if this will help you, but I wrote a tutorial on how to setup a local registry on the LAN on a Fedora Server or RHEL-compatible server. https://techne.hyperreal.coffee/tutorials/setup-a-lan-container-registry-with-podman-and-self-signed-certs/

But anyway, it's unlikely docker.io or quay.io or ghcr.io will go completely offline. If anything they might experience a DDoS, in which case I imagine they have competent devops employees who would ensure they become functional again within a matter of hours.

Isn’t a Docker registry just HTTP? Would a caching proxy be too hard to use for this?