Last summer I tossed out 3-1# bags of black eyed peas to grow as a cover crop. Watered them in well and kept watering from time to time. They grew in just great. I harvested and used the peas for a nice batch of Hoppin' John on New Year's Day. Just chop the plant off, as you stated above, don't pull the roots. The legume adds nitrogen to the soil and the roots aerate. I now have some crimson clover just coming in for a winter crop.

What island HGG? I live on Kauai for nearly 10 years, '93 to '01. Loved it but we were tired of renting and could not afford a home there.

HTH.

The University of Hawaii Cooperative Extension Service would have better information about what cover crops would do best in Hawaii than most of us would. Some differentiate between "cover crops" and "green manure crops" although there is not that much difference in reality. Generally a cover crop is left in place longer than a green manure crop. Maybe this link will help as well.
http://www.ctahr.hawaii.edu/sustainag/Database.asp

Here is a link that might be useful: University of Hawaii CES