It looks like bacterial spot. It has a typical "greasy" look to it.
http://www.apsnet.org/edcenter/intropp/ ... lspot.aspx
Options are limited as some of the bacterial spots may be resistant to copper sulfate unless you add a second fungicide like mancozeb (dithane) to create synergy. If you have other tomatoes or peppers in te same bed it might be better to pull the plant before it can infect the others. Sanitation and removal of diseased plants and leaves is sometimes the better choice since the disease is hard to stop once it starts. The good news is that the disease does not persist without a living host so keep an eye on the other plants and make sure they are not infected either. Humid and long periods of wet weather will exacerbate things. You may have to put up some kind of tent to keep the rain off the plants and put a fan out early in the day to dry the leaves off.
Fungicides don't work well after the fact but copper can build up in the soil so use it sparingly. I read that it can be mixed with dithane, but I could not find a formulation but it might be useful to alternate the fungicides instead. Not as effective but might be better than using only one in case of resistance.
Copper sulfate in combination with dithane can be used prophylactically when the weather is wet and humid. Read the label to determine days to harvest.
The bacteria will be passed on in seeds so it is important to get clean seeds. Seeds can be treated with a bleach disinfectant or hot water treatment before planting to disinfect the seeds.
http://vegetablemdonline.ppath.cornell. ... ctSeed.htm
Something else you can try as a preventive would be
baking soda 4 tsp baking soda + 1 tsp insecticidal soap per gallon of water. Spray the both sides of the leaves. Must repeat after rain and once every 3-7 days when weather conditions are wet and humid.
Got Milk? Milk spray = 1 part skim milk + 9 parts water in a spray bottle, spray all surfaces of the leaves once a week can be an effective low cost preventive fungicide when weather conditions are ripe for fungal growth.
Happy gardening in Hawaii. Gardens are where people grow.