Pixiv is a great source for original KK content, I recommend you try it

Search Tags

You can search for KK content using these tags in the Pixiv search bar:
キャラ配布(コイカツ) Character Release
衣装配布(コイカツ) Costume Distribution
シーン配布(コイカツ!) Scene Distribution (both static poses and animations)
(Add うごイラ or ugoira for animated only, but not all use these)
MOD配布(コイカツ) Mod Distribution (not character mods)

You can also replace コイカツ to コイカツサンシャイン to search for KK Sunshine content. They usually also use the regular コイカツ tags, but some do not. KKS content is mostly compatible with KK, so it's an extra source of content

Finding a specific Character / Outfit / Map / StudioItem / StudioScene

First, find the Japanese tag for the subject you are looking for. Search the English name in the Pixiv search bar, for example Megumin from Konosuba:

If you don't get what you want there just press Enter , click one of the results, and check its tags under the description. The Japanese name is usually there with the English one but not always, keep trying different post until you find it.

Then use that name in the search bar, add a space, and the appropriate tag listed above. You can use multiple names (ex. for themes of a scene/animation).

Downloading the content

KK content is usually stored in "cards", special .png files with extra data read by the game. You can usually know that a post includes downloadable content by its usage of one or more of the above tags.

If a card necessitates a mod, it will usually be in a link in the description, can be MEGA or other storage platforms, a Fanbox link, a Patreon link (not all Patreon stuff is paid stuff), etc. Sometimes, creators will have a link to their distribution platform in their Pixiv profile, so check there if a post is tagged as content distribution but you can't find how to download it.

As a Pixiv image

On Pixiv the downloadable card will often be one of the pictures in the post, usually the last picture(s) or the first one but not always. See if the description says something like "the last image is the card" OR it looks like a card (usually not a full size image like the others, single character, can have a border, sometimes has a signature).

To download a card that is an image, right-click it and use save link as , NOT save image as, very important. The name of the file should look like this 13299902_p10.png. The numbers vary, but the format must be the same. If it's not that XXX_pX.png format, then you messed up.

As an external resource link

The card can be stored on MEGA, Patreon, Fanbox, or other sites. Some will be paid content, some will be free, some will be both (ex. free outfit card and mod but paid character).

The link can bring you to a .png card, but it can also be a zip/7z/rar archive file that contains the card(s), mod(s), and original texture(s) (you don't need that last one).

About StudioItems and Maps

StudioItems (ex. character weapon) can be bundled in a mod and added via add>Item in Studio, but they can also be distributed as a StudioScene card that you are meant to import into your scene using System>Load>Import.

It's the same for maps, can be in add>Item

a StudioScene

but also a map in add>Map.

Missing mods

Finding missing mods

Bonus

I pretty much only bookmark KK content on Pixiv, check them out if you want to just browse KK content in general. Characters are mostly free, scenes and animations are more 50/50