This is assuming you aren't going for a clean slate with Goombario, of course.
A note on canon, first: Generally, Goombario is unchanged from canon, aside from the age gaps between him and other characters being shortened. The only big canon change is that he wasn't named directly after Mario. This just turned out to be a coincidence.
I can draw out his human design if needed, although you're welcome to change it around a lot.
Friends with:
Mario (continues to idolize him; there was a brief time where he doubted Mario even cared about him and others (this was when the first Mario was dropped with no IC goodbye), but it's since passed)
Parakarry (out of the PM group, they're probably the closest complete with the muns joking about Ho Yay; they talk a lot, Parakarry acts like an overprotective big brother, and Goombario snarks about him being a mother hen)
Kooper (also good buddy; sometimes they team up and harass Parakarry together for the laughs)
Watt (she sort of reminds him of his sister, and is the only partner that's younger than him (unless a Bombette player comes and changes that); he helps her out when he can)
Everyone on football team (supposedly, since it'd be offscreen. It'd make sense for him to have friends there, though.)
Nester (GAMING BUDDIES YAY)
Buddy-buddy with:
Peach (respects her lots as his princess, but hasn't spoken with her a lot)
Mir/Shadow Kirby (the only roommate Goombario has kept for a significant amount of time; they found out they both like exploring, and Goombario was considering asking if they could do just that before I dropped him)
Knuckles (gets a mention because there was an awesome maneuver in a football game and there were explosions and it was great. Also, Goombario had nominated him for vice president of the Student Council because he seemed to be the most responsible non-Peach person for that.)
Other gaming club members (they don't meet up as much, so it isn't quite as tight)
Hojita/Bulbmin (met during Zoology field trip; he used a fire extinguisher on a Fire Imp that was about to attack her)
Leon (not in game, and may be reset if reapped; old Zoology teacher and humanization counselor; had a running gag where Goombario was so unbalanced as a human at first that he couldn't give high fives)
Goroh (Driver's Ed teacher; the class is dangerous, but it's a fun dangerous. The ability to capslock rubs off on Goombario once in a while.)
Cold around:
Bowser, General Guy, Tubba Blubba (He avoids confrontation if possible, but won't hesitate to snark at them. Completely unaware of how Tubba views his and Mario's actions.)
Dimentio (out of game; nearly got him a failing grade for a team assignment in Zoology, which was bad enough. Then the whole Floro Sprout thing happened and the annoyance became outright anger.)
Luigi (not in game; tries hard to forgive him for his own role with the Floro Sprouts, since he's Mario's, but finds it hard to do)
Daisy (does not mean to avoid her, but it's a complicated story. Simplified: He had a crush on the first Daisy, who went through all kinds of drama. Upon being told that was just a clone, he became rather depressed for a while (this was compounded with getting mindscrewed during the Aparoid War and Mario leaving again) and decided it was easier to avoid this Daisy. If cornered, though, he won't be unfriendly.)
Fang (gdit fang you kleptomaniac. Attempted to use a spar to exact his revenge, but Goombario lost badly due to lack of long-range abilities)
(Liquid) Ocelot (not in game, was old...Battle Tactics teacher? Crap, I forgot, I'll come back and fix this. But he was crazy and harsh and often had his students do unfun dangerous things, so Goombario didn't like him too much)
Dating:
NO ONE THIS IS AN ETERNAL VIRGIN
Family:
Completely off-screen, and have chosen to use the free tuition option the school gained after the Aparoid War. They're split on the issue of whether it was right for Goombario to leave school temporarily to join The Master on his training.
Also has a pet Skulltula named Frankly, from a Sex Ed project. This was co-parented by Goombella, who has since been dropped and reset (so she has not had any role in raising it). Frankly was dropped off at a zoo, and future Goombario-mun can leave him there for good if desired.
Let me know if I forgot someone. I'll work on IC posts later.