Wow, a post I can contribute to with some degree of confidence!
Pik and Ni are glossed as ‘plane surface’ and ‘coconut’ in The Marshallese-English Dictionary-- and according to Abo, Bender, Cappele & DeBrum, Pik,Ni is the origin of the place name Pikinni. I guess the real mystery, however, is why the Marshallese opted to single that particular islet out for that specific feature, when nearly all the other islets in the whole of the group share almost identical features: namely, a flat surface where coconuts are growing.
There is another gloss for Pik, and that is to fly, as in the flight of birds, or flapping. Given the tendency to name places for an apparently arbitrary, isolated event, this seems like it could also be a possibility—perhaps in a storm or what have you; that’s pure speculation on on my part, however.
As for stress, I would offer that PIK(ih)NI was probably the original pronunciation—for a couple reasons.
1. I’m willing to bet that the second ‘i’ in Pikinni/bikini is actually just an excrescent vowel. Bender writes in Spoken Marshallese (Pg 60)
As you may have noted already, consonant clusters go against the grain of Marshallese phonetic habits. This is not a matter of genetics or physical ability, but of (language) custom. It stems from the patterns present in the Malayo-Polynesian parent language. The only clusters permitted without the insertion of a short, excrescent vowel are of identical consonants or closely related ones.
For instance, the Marshallese word for ‘doctor’ is taktõ (dahkduh)—borrowed from English. It is pronounced, however, as DAHK(ih)Duh. A non-loan word, jerbal follows the same pattern. It is pronounced JEHR(ih)bahl.
So you’re probably looking at the name actually being Pikni, with the excrescent vowel inserted between the two parts to help it conform to custom. Other place names also follow this pattern: Lorilejmaan (lor/un “sleeping place"+ lejmaan “legendary woman"), Eañdetdet (ean “shell” + det “redup. of sunny northside"), and Lonamonke (nam “secondary lagoon” + ke “porpoises”, to name a few. All of which also feature excrescent vowels in between their consonant clusters: between the j and the m, in Lorilejmaan; the n and the d, and also the t and the d in Eañdetdet; and between the n and the k in Lamononke.
2. The ‘N’ in Ni, is a heavier ‘n’—the doubling in the current spelling (Pikinni) is probably to reflect that (although they have recently switched to using a cedilla beneath the heavy consonants to indicate this). So while the stress would be placed on Pik, the weight of the ‘n’ would give that syllable a stress of its own.
Its worth mentioning, though, that the current pronunciation of Pikinni seems like it has changed to match the one common to English speakers (biKIni). I offer that with the caveat that I have only been in contact with Marshallese who have relocated to the U.S. (although most very, very recently)—so it may just be that group, while native Marshallese are “keepin it real.”
Also, for languagehat, I had to do a doubletake when I saw that the blog that prompted your query was called Piloklok, because in Marshallese, loklok is a “vulgar term,” technically meaning to wash one’s (female) genitals, but in current usage essentially means ‘to fuck;’ and Pi is the Marshallese transliteration for English word Bee. So I was scratching my head there for a minute. But apparently Kennedy just made it up, so chalk it up to crazy coincidence.
(Edited to add examples of other islet place names)