WARNING: LONG-WINDED FIRE EMBLEM SHIPPING INCOMING
Well, a couple of the kids have similar traits to some of the possible parents, so my headcanon pairs those up.
Inigo's a womaniser, for instance? Hello, Virion! Taciturn lone wolf Gerome? Lon'qu sound familiar? Nah's fairly sensible, and a bit lacking in the sense-of-humour department. Next thing you know she'll be telling people to pick a god and pray...
Of course, some kids don't match up quite so well, like Laurent. His character traits come mostly from his mother, so I have no strong preference for his father. I like Sully/Stahl and Ricken/Maribelle pretty much on principle. And who better to pair with the Avatar of Destruction than the Random Number Goddess herself?
So, to summarise:
Chrom/Sumia
Virion/Olivia
Lon'qu/Cherche
Frederick/Nowi
Stahl/Sully
Ricken/Maribelle
Robin/Anna
Henry/Lissa (there's a blood theme going on with Owain)
Gaius/Panne (Yarne's a coward, like a thief...? OK, a bit of a stretch)
Vaike/Tharja (I want to see him suffer. :-p)
Gregor/Cordelia (the only first-gen male mercenary)
Libra/Miriel (because only Libra would have the patience to put up with Miriel's eccentricities)
And I have no preference for second-gen pairings, though I will throw out the pairs that got me through Apotheosis:
Cynthia/Gerome
Brady/Lucina
Morgan/Owain
Severa/Inigo
Plus I used Laurent/Lucina to finish Lunatic+, so that's another option...

They're both just so sweet, and watching Owain confuse the nonsense out of Donny is a lot of fun.

Oh man, this is my jam.

First generation characters

Chrom / Sumia : it's canon, okay? Galeforce / Rightful King works with Aether super well on both Lucina and Cynthia. Plus, Cynthia's Chrom recruit lines are hilarious.

Kellam / Sully : enjoy your unkillable Kjelle. Aegis and Pavise OP.

Henry / Tharja : the two lovable maniacs, together forever. Vengeance Lifetaker Noire 2 stronk.

Virion / Olivia : for the sole purpose of justifying Inigo's behaviour. Also, Inigo's hair.

Donnel / Nowi : makes manakete!Nah absolutely monstrous with incredible growth potential.

Lissa / Lon'qu : it's so cute! Perfect for Owen's growth stats, too.

Miriel / Libra : makes Laurent a little less squishy with 30% HP recovery at the start of every turn.

Maribelle / Ricken : To give Brady as much magical potential and to give him a recovery option in Lifetaker or Renewal.

Stahl / Cherche : another really cute pairing. Also, this.

Gregor / Panne : gives quite a bit of durability to Yarne and gives him quite a lot of good class options.

Cordelia / Gaius : the knight and the scoundrel. Makes Severa a highly versatile and mobile unit with Galeforce and Assassinate.

Male!Avatar / Spoiler : follow the link to reveal the spoiler. Gives birth to a monstrously good magic-focused Morgan. All together now: awww...

Female!Avatar / Kellam : the only ending which ends up in the history books remembering Kellam's name.


Second generation pairings

Lucina / Male!Morgan : let's face it, Lucina needs a cheerful presence in her life after all the crap she's been though. Morgan does just that.

Laurent / Cynthia : hilarious support between the straightest of straight men and the most airy heroic of pegasus knights. They complement each other perfectly.

Owain / Severa : concrete proof that opposites attract.

Yarne / Nah : a heroic tale featuring a killer rabbit.

Noire / Brady : I think it's the only pairing which doesn't feature Noire blowing up. That's how good it is.

Kjelle / Gerome: their rivalry is eternal-- and so is their bond. Also makes Kjelle even more unkillable and highly mobile.

Female!Morgan / Gerome : he takes off the mask!


Forever Alone: Inigo.

Best male / male support : Owain / Inigo. Sparks will fly!

Best female / female support : Tiki / Female!Avatar. Curiosity killed the cat.