"...if Ron was going to begin calling her 'Lav-Lav', he [Harry] would have to put his foot down."
Bill and Fleur fit this trope as well, especially if you ask Ginny and Hermione.
When contemplating the idea of Ron and Hermione getting together, Harry fears (among other things) that they might turn out like this, using Bill and Fleur as an example. Sadly, the series ends before we find out.
Parodied in one of the J.W. Wells & Co. novels by Tom Holt, where a bickering couple are tricked into overdosing on love potion. They start using pet names at the end of every sentence but retain their normal personalities, leading to sentences like, "Don't be such a bloody idiot, honey-bunny".
Every vampire couple. The only human couples worth mentioning are either broken up (Bella's parents, Jessica and Mike), basically nonexistent (Angela and Ben), or barely begun by the end of the series (Charlie and Sue Clearwater).
The werewolves and the girls that they imprint on. To the point in which the other wolves in the pack do not look forward to mindlinking with a wolf who had just been visiting his imprintee.
In the second book of the Guardians of Ga'Hoole series, the Band comes across a pair of sooty owls that do not give their names but refer to each other as Sweetums and Swatums. They preen each other and talk about eating sugar gliders (which taste very good to them but are too sweet for other owls) while speaking to the group.
In Salman Rushdie's Haroun and the Sea of Stories Prince Bolo and Princess Batcheat are like this, to the disgust of absolutely everyone around them. Bolo is so oblivious (and stupid) that he constantly praises the silly Batcheat for her beauty and her singing voice, both of which are described in detail as completely horrendous.
Tales of Kolmar: As newlyweds, Lanen and Varien are like this, with Jamie even hanging a lampshade on it and them teasing each other about trying to tone it down in front of him. However, they do find difficulties, pains and sorrows and arguments that can't be soothed away with a touch or a few words, and eventually the relationship smooths into Happily Married. They still get silly sometimes, but Lanen notes that their bond is more complex now.
Crown Prince Roger and his girlfriend Rivka in the Honor Harrington novel Ashes of Victory, though they're not seen onscreen; the Queen's chief bodyguard calls them "unbearable adolescent goo". When they do get actual screen time in A Rising Thunder for their wedding, they've gotten over it.
In A Civil Campaign Rene and Tatya Vorbretten are cuter than cute together. And they're Barrayarans. What is Barrayar coming to?
In Wolf Hall, Henry VIII and Anne Boleyn oscillate between this and arguing, with little in-between. Thomas Cromwell privately finds the latter easier to take than the "billing and cooing" but as we all know, that took a rather dark turn.
The Stormlight Archive: Shallan and Adolin become this within about five minutes of meeting each other, especially from Kaladin's perspective — though he admits he's probably just being overly cynical. Even Shallan realizes it, and is rather embarrassed, but Adolin seems happily oblivious.