I understand from some Hawaii Island contacts that there is a county ordinance or law that prohibits shooting even on public land. One of the activists there who has been trying to get a public range funded/approved was telling me that even in hunting areas you can't just shoot, say to zero in your scope/rifle, so any shooting has to be at the animal being hunted. He also told me that have been a couple of citations issued for target practice on private land.
I am not an expert here and do not offer these statements as fact and each person should verify all information for themselves. Having said that I believe the target shooting in hunting areas not being allowed is correct. But there are many restrictions like discharging a firearm outside of valid hunting dates and times and anyone discharging a firearm must have a valid hunting permit. Of course there are many other firearms related restrictions in regards to public hunting lands that one could violate and be cited for. You can also hunt on private AG lands and there are even permits that agricultural land owners can obtain which when verified, allows them to take certain animals that are deemed "nuisance" or cause "crop damage". These permits are generally year round, up to no limits and can be day or night.
As for shooting on private land, if the land is zoned as "residential" you can almost certainly be looking at potential reckless endangering issues or charges due to the "residential" wording in the law and the zoning. If the land is zoned as AG or agricultural then you have more options, but I am not going to give out any advice here that can be misunderstood. I will note that the AG zoning, "recklessness" and target shooting on a "target range" are key things to consider or research. My parents are semi-retired ranchers on the Big Island who have their own shooting area. Other family relations own a very large and well known ranch on the BI and they have a range, even utilized by LE in the past. Many Ranches have private shooting areas, this is not just the Big Island but also happens on Oahu. I have done shooting in a professional capacity here on Oahu on one private ranch and with more frequency in a personal capacity on another private ranch. I know of another large ranch on the island that has a range and is utilized by another group or "club". Of course I am aware of other so called "private" ranges on this island, but the legitimacy is a bit more in question.
Again I might reference Crazy Kat for more input on the Big Island as she has mentioned several times about her relationship with the Big Island Gun Club which is located on private AG land on the in the Puna district, Glenwood / Mt View area. I believe that club has had more interactions with local entities in regards to the legitimacy of such a range and as far as I know they are still active. I wouldn't mind hearing more from her on this topic also.