Wouldn't quite call these rare, but they're relatively uncommon:
CrystalShipping (EusinexCrystal): I've actually met many people who ship it, but despite the fact there's a decent amount of fan art, there are practically no fanfics for it. Aside my own, I've encountered only two or three others-two of which included it but didn't focus on it as the primary shipping.
CheckmateShipping (Cherenxfemale BW player character): Like with CrystalShipping, there's a decent amount of fan art for it, and a decent number of people ship it but I have yet to see a CheckmateShipping fanfic, only part of one drabble.
HoennChampionShipping (Steven StonexMay): It's not rare per se, but I've only ever seen one fanfiction for it and only a little fan art.
ComfortShipping/AccidentalShipping (GoldxWhitney): Whether games or manga, I adore this pairing. Gold and Whitney look so cute together! Manga-wise their personalities are perfect for eachother and they have a really entertaining chemistry.
DiamondShipping: I see it as more of a in-the-past-ship, but nonetheless it brings up a lot of intriguing possibilities. I've always liked the idea of Ash's father being Giovanni (and I heard that way back the makers of the anime considered making that canon), and that would definitely explain why Delia is so vague about the identity of Ash's father...and I think she mentioned in one episode that Ash's father is from Viridian City. That would also make Ash the alternate-continuity half-brother of Silver (someone needs to write a fanfic about that).
NewRivalShipping (WallyxMay): Why does nobody ship this? I have never met anyone else who ships this pairing until today, yet I adore it and it seems like it should be a major pairing.
SteelShipping (AttilaxHun): To be honest, I like all the Team Rocket male/female duo shippings (also like RocketShipping and NeoRocketShipping, and manga-wise I like RocketMasakudoShipping, the rather wordy name for KeanexChermaine). Due to their erm, steely, personalities Attila and Hun would have a really intriguing relationship; I wonder if they'd be cold and harsh towards eachother all the time or if when no one else is around they act more affectionate. They also remind me a little bit of AntagonistShipping (Pokemon Adventures Sabrina and Lt. Surge), another pairing I find intriguing.