Candy Kong – Donkey Kong’s rumored girlfriend. 
I was so sure she was his cousin. I have no idea why. But yes, okay, I can buy into that relationship.

Chunky Kong – Kiddy Kong’s older brother, Dixie and Tiny Kong’s cousin.
This seems reasonable.

Cranky Kong – Wrinkly Kong’s widower and elder of the Kongs. He is the original “Donkey Kong” from the 1981 arcade game of the same name.
WHAT
HOW IS CRANKY KONG THE ORIGINAL DONKEY KONG
HIS NAME ISN’T EVEN DONKEY KONG

Diddy Kong – Donkey Kong’s nephew. Dixie Kong’s boyfriend
Oh, wow, I was deeply sure he was Donkey Kong’s little brother. This is tough.

Dixie Kong – Tiny Kong’s older sister, Kiddy and Chunky Kong’s cousin, and Diddy Kong’s girlfriend
I definitely thought she was Kiddy’s sister — Kiddy was the one who wore the footie pajamas in DK3, right? — and Tiny’s cousin.

Donkey Kong – Cranky and Wrinkly Kong’s grandson, Diddy Kong’s uncle and best friend, Candy Kong’s rumored boyfriend and the ruler of DK Island.
OH MY GOD HIS GRANDSON
I THOUGHT CRANKY WAS HIS DAD
WHO ARE HIS PARENTS
WHO ARE DONKEY KONG’S PARENTS

Donkey Kong Jr./Baby Donkey Kong – Implied to be the current Donkey Kong or his father.
What

Funky Kong – Donkey Kong’s brother and friend of the Kongs.
They’re brothers? How is Funky Kong Donkey’s brother and Diddy is only his nephew? Funky and Donkey barely even talk.

Kiddy Kong – Chunky Kong’s little brother, as well as Dixie and Tiny Kong’s cousin.
Fine. Fine. That’s fine. That’s probably fine. Sure.

Lanky Kong – Distant cousin, described by Cranky as “a twisted twig on a distant branch of the family tree.”
This is perfectly reasonable.

Swanky Kong – Direct relation unknown (possibly a cousin of some sort to Donkey Kong).
Yes. I believe this. Finally getting back on solid ground, here.

Tiny Kong – Dixie Kong’s younger sister, Kiddy and Chunky Kong’s cousin.
Okay, okay, okay. So it’s Donkey Kong (parentage unknown) and Funky Kong who are brothers. Their nephew is Diddy; he has no siblings. One set of Diddy’s cousins are Dixie and Tiny. Another — separate — set of cousins are Kiddy and Chunky. Is this even close?

Wrinkly Kong – Cranky Kong’s now deceased wife and Donkey Kong’s grandmother.
WHEN DID SHE DIE I DON’T REMEMBER HER DYING THE LAST I REMEMBER SHE WAS SITTING IN HER LITTLE CAVE WITH ALL THE BANANA FAIRIES

Also: “Manky Kongs are enemies in Donkey Kong Country. They are the only Kongs in Donkey Kong Country that are an enemy. In fact, these orangutans are described as Kong reject orangutans, implying that they’ve been exiled from the Kong Family. This is due to their betrayal of the Primate Alliance during The Great Ape War.”

“Lanky looks very similar to Manky Kongs, but unlike them he is on the good side.”

Guys, it’s been a really hard week and this just put me over the top. Be gentle; be kind, explain this slowly to me.

[All information via Donkey Kong Wiki]