I bought the FabriCoat paint on Amazon, but you could try your local craft shop.
If you've never used this before i'd advise you do a test run first on a scrap piece of material, just to get some practise in.
Just follow the procedure in the video below and you won't go wrong. As the coat is only a small piece you won't need to use a whole lot of paint.
I used a small paint brush and sponge to apply it. Then an old tooth brush and nail brush to work it into the fabric. The most important part is to make sure the coat is nice and damp before you start painting.
Don't worry if you see a blotchy/patchy look after the first application. Dampen the coat down again with water and apply a second coat of paint, again using the same procedure with a tooth/nail brush to work the paint into the fabric.
And don't worry that you might do damage to the coat fabric with the nail brush. I gave my coat a good scrubbing over multiple times with no damage. Just be careful around the wee coat buttons
.
Amazon link.
https://www.amazon.co.uk/Fabricoat-...t+fabric+dark+brown+paint,aps,203&sr=8-5&th=1
The tie is from the old Character Options figure.