Other carbon sources around the house : egg cartons. I reuse them for eggs and they can be used to start seeds, but when they get old and stained, they are a good addition to compost.
It is important if you want to get hot compost to balance the greens and browns. Newspapers, cartons, and such are very high carbon so you don't want a lot of that. Plant stems, bark chips and things that are less processed will have a lower C:N ratio. You want the final pile to be 25:1 (C:N) ratio otherwise it will cold compost and not be thermophillic. Good sources of N are greens but you can use fresh manures (cow, sheep, goats, swine, rabbit, but not carnivores) Horses are wormed and the wormers may persist but it can be used but should be composted because it has a lot of weed seeds. Fertilizer is a good way to boost the nitrogen content of the pile and heat it up. The bacteria don't really care about the source if it is synthetic or not but if you want to stay more organic blood meal, feather meal, crabmeal, alfalfa meal (horse food pellets), fish emulsion or fish meal, cottonseed meal, and soybean meal are the better sources of nitrogen.
People don't really understand organic.
Organic gardens should feed the soil so the soil can in turn feed the plants. Inputs must balance outputs to be sustainable. If it takes more inputs than what the soil can provide to grow a crop then it is not organic because you are essentially feeding the crop and not the soil.
When making a compost pile you are creating an environment to grow the soil organisms. Those organisms need a balance of nitrogen, carbon, air and water in order to grow.
You cannot make a pile only out of carbon, and if you make a pile only of nitrogen you will get a slimy, smelly mess. If you cut a tree and chip it branches and leaves you will end up with a pretty balanced pile of greens and browns but it is from a single source. It is better to have trees of different kinds chipped and mixed in a pile so you will have a balanced source of nutrients. Better yet to have at least 5 different sources of greens and browns. The more the better.
I found making a pile slowly works but ends up being a cold pile since it does not develop the height fast enough to cook and nitrogen is quickly lost from a pile. So, it is better for me to stockpile browns and then when I have enough greens, I build the pile in a day. I get a hotter pile that finishes faster. I layer about 8 inches of brown and then 8 inches of greens and I water that down. Throw a shovel full of soil to provide the starter organisms and repeat the layers. About a foot up, I put in the air shaft and keep filling around it. I end up with a brown layer on top.
I do this pile at my community garden especially when someone has dumped illegal waste in front of my plot. At home, I don't have a lot of browns or room so I prefer vermicomposting. It is much easier since they only need to be fed once a week and I use newspaper for bedding.
Happy gardening in Hawaii. Gardens are where people grow.