Your best bet is to do the following (to almost guarantee availability)....

1) wait until about 6 months out and check then
2) EWR/HNL is a hard one to book - HNL/EWR will be 5 times harder, so get prepared to be flexible with your dates and return routing
3) to maximize your Hawai'i time, do the following:

• the evening before your official 'first day' of the trip, book your flights to go to LAX first and overnight there
• take the LAX-HNL nonstop first thing in the morning, which will get you into HNL before noon and hours before either the IAH or EWR nonstops would - you get an extra day on the Island
• For the return, book HNL-LAX-EWR or HNL-LAX-IAH-EWR and if you are an Elite member, waitlist HNL-EWR and HNL-IAH-(EWR)