So I wanted to save notes on images. Is there a tool that will let me do that? Preferably with the coordinates on the image as well.

no. at least not like they are on this site. the notes are completely separate from the image files and they cannot be integrated to the image file with any methods without changing the images into flash files or something.

My best recommendation is to simply save the image into your hard drive, then copy/paste the translated text from the notes into a text document.

Save the image, then save the e621 post with https://addons.mozilla.org/en/firefox/addon/mozilla-archive-format/
if the image file name is b420904d16cf57bc05dc6b17b701b251.png
then the e621 post should be b420904d16cf57bc05dc6b17b701b251.png.maff

edit:
never mind, the notes don't show on the archived version :-(

You could embed the image inside a SVG file along with the notes but that'd require some work (not many programs can preview SVG files) or you could try with a PDF perhaps?

If you want to save comics (probably) a PDF would be the best option

I wondered the same thing once but the only real way is to just edit the translated words onto the image itself with photoshop or something. :/ sorry.

Animus usually have .ass subtitles to contain all and every change and translation made to video, so there's no need to render stuff into video itself, meaning original content stays completely unaltered.

I did bump into .cbr format years ago, it's format for comic books specifically. It's basically regular zip or 7z file with all the pages as regular jpg or png inside it. However it can also contain additional data, including index, extra information and overlays including translations. Sadly I haven't been using that format that much so no idea how to do it in practise, but that would sound like the way to go as stuff is kept unaltered and in theory it should be possible to then create some automatic script to get stuff and put them in correct places and it's still easy to unzip it if someone doesn't have proper reader installed.

After that there are pdf, which is more mainstream standard and also allows having notes and such on pages. However for some reason I have the feeling that approach isn't good.

It doesn't have to be embedded, I don't plan to view them.

I just want to save it, so maybe when I need to I can use the data to restore or embed to images. So raw data of coordinates would be fine.
There should be coordinates relative to the image saved so the notes can be rendered

You can get the notes for a specific post in xml format through the API.

https://e621.net/note/index.xml?post_id=879662 contains the notes for post 879662

Should be able to just save that page along side the saved image.