It's easier to search the flight legs individually - sometimes the united site gets confused with tricky flights.
Search one-way NYC -> KOA, and then LIH -> NYC and use the award calendar to figure out available dates.
After you know which ones you want, enter those dates into the multi-destination search, and it should work.
If it still doesn't, you can call them to book - have the flight numbers you want handy, and they should be able to help you.
Also, you can search the connections individually too - for example NYC -> LAX, LAX -> KOA. (or SFO).
If you can't get the site to put them together for you, you can call to book.
You can use Dan's excellent guide here to see which islands are served from which connection cities:
http://www.dansdeals.com/archives/62063