OK, well, lots of experimenting, but this is what I have ended up with.
Antler is very resistant to staining and to painting, even these stains have only sat on the surface. The branches and leaves have been picked out with an acrylic ink, heavily cut with thinners, and the owl has been coloured with a stain known as ‘Yashabushi’ – alder cones boiled down for an hour give a yellow/brown dye, then some iron oxide (rusty screws and nails) react with the tannic acid in the dye to darken it – the more iron oxide, the darker the colour. The dye should also be left to age – the older it is the better it works (apparently). The final touch was to apply a clear wax and warm with a hair drier to pull the wax into the carving and protect against dirt.
I am deeply indebted to the contributers to the Carving Path forum (see links) without whom this project would not have been completed.