There are many ways to paint latex puppets, the most popular of which is to use PAX (a mixture of artists' acrylic paints, such as Liquitex, and a prosthetic adhesive called ProsAide, of which the non-sticky version, NoTack, is said to be the best).
However, I decided to opt for colouring the latex itself with the base colour, and will use PAX later to dull down the uniform colouring and add character. I added some latex colourant (available from the model supplies shop 4D in Aldgate, London) to a batch of liquid latex and cast new skins.
The rest of the liquid latex can be kept in an air-tight container and will be used to colour the tentacles and make new skin sections to patch the main puppet skins when the model is finally put together.
Meanwhile, this is what the main skins look like...