There are two sites I have found that can help you find records online. The first website is ulukau.org. It is in the Hawaiian language but there is a button at the top right to get the English Text. Click Genealogy and then click Browse and you will see a listing of Indexes. Unfortunately the only index with dates listed is for Marriages. Depending on the island the dates range from 1826-1929.
The other online website you will have to access through Google. Unfortunately you can only find death records, type in the Search box, online hawaii death index. In the search results find Online Hawaii Death Records Indexes-Online Searchable.. Click this and you will be directed to Hawaii Death Indexes & Records. Look for Honolulu Advertiser & Honolulu Star-Bulletin Obituaries 1994-2012 in the listing. Click this link and on the next page you can enter the year and first letter of the Surname. You will be accessing Obituaries that were mainly printed in the two major Honolulu newspapers.
I decided to look for my Mom's obit since I know it was printed in the Star-Bulletin so I looked for 2006 and put the first letter "O". Her obit was not listed so if you do use this site you may or may not find what you are looking for. As far as I know these are the only two absolutely free online websites I have found.
The only way you can access these records is if you live in Hawaii or you know someone who does live here. The best place to search for Birth, Marriage and Death records is the Hawaii State Library System. Most libraries have these indexes on Microfilm. All records start with July 1909 and most end in December 1948. The main library in Downtown Honolulu also has copies of Birth, Marriage and Death Certificates on Microfilm. Most are from July 1909 till December 1920. You can also access Obituaries from all Island newspapers via Microfilm, some Obits dating back to 1920
Hawaii Birth, Marriage and Death records are the hardest to access online for free. I can access Ancestry for free while in the Library and even then I get no results if I want to find a death date for anyone before 1962. After 1962 you can find a person through the Social Security Death Index (SSDI).
For some reason I guess Privacy issues are the main reason Hawaii does not put their records online unlike other US States. I can easily find Vital records free online for States like Washington, California, Minnesota and Illinois. Heck, I can find copies of Death Certificates for residents of Missouri (1910-1963).
This is one of the many challenges Genealogists face when searching the Internet. Some records will be found but many others will not but that will NOT stop anyone determined to find out.