A small part of the joke of "ainokea" is that it looks like it should be a proper Hawaiian word, but in fact it is a phrase in the local dialect of English written to make it look like it comes from the Hawaiian language. There are very few people who can actually have a conversation in Hawaiian anymore. The three basic groups of people who can are the elderly, university students, and the kids who enroll in Hawaiian Language Immersion Programs, in which math and other classes are taught using the Hawaiian language instead of English. Kids can now take classes in Hawaiian Language Immersion Programs from kindergarten through high school.
Instead, the vast majority of people who grow up in Hawaii speak a dialect of English that mixes words and structures from Hawaiian, Chinese, and other languages in with English phrases like "da kine" or "li' dat" ("that kind", or "like that"). Among the reasons to "talk da kine" when you can speak Standard English: to mark yourself as a Local, to keep outsiders from knowing what you're talking about, and for humor. Humor is big here.
The University types call the dialect Hawaiian Creole English, but most of the people who actually speak the dialect only use that phrase when they're making fun of the University types. Instead, the native speakers call the dialect "Pidgin".
In addition to being the Pidgin/Hawaiian Creole English version of "I don't care", Ainokea is the name of a company that manufactures surfwear. One T-shirt popular in Hawaii a couple of years ago said, "How's my surfing? Call 1-800-AINOKEA."
At least one non-profit organization in the islands has raised funds by selling T-shirts that say, "AIKEA".