Pax paint is generally the go to for painting latex and what's typically recommended. For brushing on it's usually a 1:1 mix of pros-aide adhesive and acrylic paint (it has to be acrylic, don't use oil paints for this), if you want to run it through an airbrush then thin the acrylic with water first then mix with the pros-aide. There's a couple different brands that make pros-aide and most offer a couple versions, the original, a newer formulation, and a no tack version. Any version works just fine for our application here. Also after the pax has dried it's usually a good idea to lightly dust it with talc and brush it off to reduce the sheen and tackiness.
Another common method is to make rubber cement paint. It tends to be more durable than pax and has a lot more flexibility to it. Although you should only spray rubber cement paint if you have a dedicated work space (not a shared living space or bedroom studio) with plenty of ventilation and adequate respirator, it's pretty nasty stuff especially when sprayed. The basic run down of rubber cement paint is a mix of rubber cement (something like this https://www.amazon.com/Best-Test-Premium-Paper-Cement-16OZ/dp/B004O...) oil paint (do not use acrylics for this method) and naptha. First thin the rubber cement with naptha, you can kind of eyeball it to a slightly thinner milk-ish consistency somewhere around a 1:3-1:4 ratio (if I remember correctly) depending on if you're brushing or spraying it, then add the oil paint. I usually mix a batch of the thinned cement in a canning jar then pour out a little bit as I need it into smaller cups to mix the paint in. After applying rubber cement paint you want to seal it with a rubber cement sealer like V-Matte (https://www.frendsbeauty.com/v-matte-rubber-cement-sealer.html).
I used rubber cement paint a long time ago, and it seemed to be stretchier and had less tendency to wrinkle when applied to foam latex compared to PAX. I think I used universal pigments (like the ones at the paint shop, used to tint both enamel and acrylic wall paint) to colour it. Probably pigments made for silicone rubber would also work well. I mostly thinned it with naphtha and airbrushed it.
Pax is more like using paint, and is easy to get a nice finish, but recuse it is slightly firmer than the foam latex underneath, it can form small wrinkles when the puppet bends. On liquid latex skins this is not such an issue.
I've just ordered a 4 oz bottle of Elmer's Rubber Cement from Amazon. You don't use large quantities, so that should be enough. The BestTest Paper Cement in the link is a large amount, and not available for shipping to Australia anyway. I want to also test it as a flocking glue, though it may dry too quickly to be suitable for that.