Cocobolo gets me too. Took a while to get sensitivity to it, but it got me eventually. I get eczema on my neck, hands, wrists, inside elbows, regardless of where the dust touches me.
I still use it but I wear a respirator, use dust collection and a hanging air filter, wear long sleeves, never work with it in warm weather (pores opened up from sweating) and I shower afterwards.
I do this with any rosewoods because I find I'm allergic to them all now. And I wear a respirator regardless of wood type.
Lastly, I try to use hand tools or tools that cut and make shavings instead of tools that make dust.