The HOA does not restrict long term rentals.

If the property is in an HOA/COA notify them. 

I attended to rent it out on airbnb but the HOA didn't allow it.

Even with the high HOA fee it was still net positive cash flowing of about $500/month

I know the HOAs in Hawai'i are fairly steep ($500-$5000) but I feel that if you found a leasehold property with a cheaper HOA fee, then it would be feasible to pay off say a 30yr fixed mortgage payment + HOA + lease rent (not sure if lease rent applies in all cases) every month ( or at least most of it).  

Depends on how much the HOA will eat into the cash flow..

I have a 3 bed 2 bath in Cary NC outside of Raleigh, its quiet, backs to trees, chill hoa. i have had it leased annually for years and i have not seen it in years, its very passive, with a manager, though not great profit. i want to change it to furnished 3 night minimum airbnb to weekly or even monthly.

She paid cash for it, but here are her yearly fees (approximate):HOA  $2600Utilities  $3000Insurance $2000Repairs/maint $2000Taxes $700CC fees (her portion) $872So about $11,200 in expenses, with a net income for her of approx. $30,000 from an investment of $270K. 

Contact your local city permit office and find out... also make sure the lot isn't part of any HOA or has any neighborhood restrictions. 

BUT taxes and HOA fees are really eating in to our income in the last few years.