Fresh clippings I think are still greens, but the bark chips will be brown. Layer them together in the compost pile with the manures, a little bit of compost or soil to provide microbe starters, add enough water to get it to the wrung out sponge stage and they should cook pretty well. I would try to get some other source materials in the pile so that it will be better balanced. You may have to make more than one starter pile so it can be managed better, unless you have a loader to turn the piles. 3-5 ft high and as long as you like in windrows.
Happy gardening in Hawaii. Gardens are where people grow.