For the original popular ship within the DCU between Dick Grayson and Starfire, the name "DickKory" is most commonly used among, though some mockingly call it "Dickfire". Also called RobStar, DickStar, NightStar (also the name of their child in Kingdom Come), Nightfire, Starwing, and multiple variations.
There's also some ships inbetween the Fab Five which include
"WonderBat" for Batman/Wonder Woman (mainly manifesting from the DCAU)
"BatLantern" for Batman/Hal Jordan.
—-
Other
Deadpool fans have nicknamed the Deadpool Skrulls, Skrullpools. For actual Deadpool shipping, how about Deadcable? Or Deable or Cadpool? Deadpool seems to be a fan of Cablepool◊, Though in a slightly different context...
In Doctor Who (Titan), an in-universe occurs in a First Doctor short strip where we discover that Shipper on Deck Susan secretly thinks of Ian and Barbara as "Barbarian". Ian doesn't get it and thinks that she's insulting humans as backwards.
Empowered dreams up quite a few of these in-universe when she learns one of her teammates is gay.
Iron Man has Pepperony for Pepper Potts and Tony Stark (although this is mostly used in MCU film fandom, not comics fandom) and Irony for Tony Stark/Sentient Armor.
Jem and the Holograms (IDW) fans refer to Stormer and her girlfriend Kimber as "Stimber". This was given a Fandom Nod in-series as they're referred to it once.
Ever since Thor and Storm started dating in Marvel Adventures Avengers, the term "Thororo" has been created.
Runaways fans don't use these too much - Xavin / Karolina might sometimes be abbreviated to "Xavolina", but it's rare. Since the advent of the Hulu show, however, some Nico Minoru / Karolina Dean fans have been pushing for "Nicolina" or "Deanoru".
If you happen to like Spider-Man's first love Gwen Stacy, you are stuck with "Gweter" or "Pwen" (although there are the slightly better-sounding alternatives of "Peten" and "Petwen"). "Doomshipping" covers all the bases.
Alternatively, if you prefer Spidey to be with MJ Watson then "Petermj" is the name of your ship.
Or, if you're reading Sins Past, Normwen Stacborn.
If you like Spidey's real first love, Betty Brant, you'd get Petty or Beter Parant (Brarker is just too uncomfortable).
"Spideypool" is the relatively recent pairing of Spider-Man and Deadpool.
Non-romantic version: Francophone Tintin fans collectively refer to Dupond & Dupont (Thompson and Thomson) as "les Dupondt", which is also used by Tintin and Haddock in the original comics.
X-Men fans seem to like this a lot, but unfortunately no matter what you ship in what series/universe, you usually come out rather badly. Jott, Scemma, Jogan, Lemma, Rogan, Robby, Kyro, Ryro, Kurtty, Lancitty, Tonda, Jonda, Xietro, AleX23, Bobbity, Bobmara, Bobbilee (or Jubby), Kurahne, Kurmanda, and a favorite, Wandurt. Apparently the character's names were not chosen to be Portmanteau Couple Name friendly.
"Pionda" (Pietro/Wanda) is not only clunky, the concept comes out badly no matter how you think of it. A preferable term would be "Panda", in case you wanted the Squick to be cute (either way, the couple is more or less canon in Ultimate Marvel).
Rogneto is about the only portmanteau that works for the X-Men that is used.
There seems to be a candy theme when it comes to shipping Storm: RoLo for Ororo/Logan, OreO (capitalization variable) for Ororo/Remy.
Ricstar seems to be the happy exception to the rule. It even has Peter David's blessing, who stated that it sounded much better than RicShat. It does.
Kuroro, for Nightcrawler/Storm, is another of the exceptions.
There has been...difficulty on comic message boards between fans of Kiotr (Kitty Pryde/Piotr Rasputin) and Kete (Kitty/Pete Wisdom)
And now thanks to All-New X-Men there's StarKat for Kitty/Peter Quill. Kitty sure loves her "Peters..."
Helix has been a term that has been thrown around to describe Hellion/X-23. Another that's come up for X-23 is Cyx-23, for the shiptease between Laura and Teen!Scott. Bonus points for suggestive pronunciation. A third one for her is Larren for Laura and teen!Warren.
Cherik seems to be the most popular name for Professor X/Magneto, although this is mainly seen among fans of the live-action films.
From Young Avengers, we have Amerikate for America Chavez / Kate Bishop, as well as Wickling for Wiccan / Hulkling.