Maui has Goats, Pigs and Axis deer. I used Maui Hunting Safaris for a goat hunt, it was pretty fun, the ranches they have access to are not the hardest walk from what I saw of them. The goat hunts also include management animals, I shot my trophy billy, a non trophy billy and an axis doe.
that was my hunt
http://www.outdoorsmenforum.ca/showthread.php?t=337955
For tukey hunting you have to go to the big island. The hunting regs on state land are fairly complex compared to Alberta, with most areas only open on the weekends depending and can be closed on days that bird hunting is allowed.
Also, get your exemption number right away or you will have to do a Hawaii hunter Ed course. You will need to send a copy of your hunter safety course, not your WIN card to the DNLR. Mine only took a couple days to get back, but it can take a few weeks.
Private land or state land requires a hunting license which is $105. Bird permit is extra
http://dlnr.hawaii.gov/recreation/hunting/