For 1.21 and up check the New Custom Paintings Resource Pack and Datapack using the new Painting variants feature

Custom paintings resource pack

This Minecraft resourcepack adds some new paintings by using the CustomModelData feature added in 1.14.

It is inspired by the custom paintings used on the Hermitcraft server, as seen in this video (14:53).

Installation

Install like any other minecraft resource pack.

Usage

The following image shows the paintings available in the resourcepack. You can also add your own.

Available paintings

To get the paintings you have two options: using the give command or using mukitanuki's Custom Roleplay Data datapack.

Give command

Use the following command to give the player the custom painting defined by the CustomModelData number.

/give @p painting{CustomModelData:<number>}

Where <number> is the painting index as defined in painting.json

mukitanuki's Custom Roleplay Data datapack

Alternatively, and more survival friendly, CurseForge user mukitanuki has created a datapack to change an items CustomModelData tag. You can download it from CurseForge.

Once installed you can run the command /trigger CustomModelData set <number> changing <number> for the index of the painting.

Check the CurseForge page for complete instructions on this datapack

Adding custom paintings

Paintings in this resourcepack are composed of 16 by 16 pixels tiles, although the texture can be upscaled.

Textures

Place your textures (in png format) into assets\minecraft\textures\item\paintings directory inside the resource pack. They can also be placed inside their own subdirectory to keep them organized.

Models

Create a new .json file for each painting you want to add in assets\minecraft\models\item\paintings. You can also place this files inside of their own subdirectory.

Copy and paste the next code into the file you just created and change the text between quotes after the following properties:

{
    "parent": "item/paintings/master_painting",
    "credit": "YOUR_NAME",
    "texture_size": [16, 16],
    "textures": {
        "0": "item/paintings/YOUR_TEXTURE",
        "1": "painting/back",
        "particle": "item/paintings/YOUR_TEXTURE"
    }
}

"credit": Change YOUR_NAME for the message to credit you with this painging.
"texture_size": Change this numbers if your painting is not 16 by 16 pixels.
"0" and "particle": Change YOUR_TEXTURE for the name of your texture withouth the .png extensions. If you placed the textures inside of a directory you also have to include it.

Adding models to the painting

Edit assets\minecraft\models\item\painting.json and add a comma after the last predicate line and paste the following code.

{"predicate": {"custom_model_data":MY_INDEX}, "model": "item/paintings/MY_MODEL"}

Change:

MY_INDEX: for the index of the new painting, make sure they are not repeated or it will override another painting.
MY_MODEL: change my model for the name of the .json file you created in the previous step, without the file extensions. If you placed your file inside of a directory remember to include it as well.

Credits

First 4 sample paintings in the resource pack are created from art released under CC0 license by ansimuz. You can find the original images at the next links: