Don't be surprised that there are no Romantic relationships involved in it.
This is all based on the personality of the characters and how would they interact with each other. And the ones that marked gray is a reference to how the animatronics from the first game and the withered ones from the second one are not the same characters.
Freddy: Being the main character, he pretty has the more balance of characters he likes and dislikes. With Bonnie, Ballon Boy, and Marionette being his best buddies; and being neutral about Toy Freddy because he sometimes can't stand his clingy & over-goofy personality.
As for being related to Golden Freddy, well the animatronic was spawned/inspired by Goldie; and when the children's spirits were in the animatronics, the child that Freddy possessed used to think that his brother was killed along with the other kids & got his spirit trapped inside Goldie (which later turn out to be not true).
Bonnie: I see Bonnie who is the kind of guy who can get along with anybody...well almost
Chica: Same thing goes for Chica, with her two BBFs being of course Toy Chica & Mangle.
Foxy: I figured that in the earlier years of the Fazbear pizzerias, Foxy was originally portrayed as one of Freddy's enemies that steals from Freddy & friends, mainly food. Like Hamburglar & Grimise were to Ronald McDonald before they eventually became friends.
Although they are friends, Foxy's still a tad jealous that he never gets to be on stage while Freddy hogs the spot-light. And he obviously doesn't like Toy Freddy, due to his (as Foxy puts it) "insufferable grinning flab-face."
Golden Freddy: Although being one of the first & eldest animatronics, in the second game, Goldie doesn't interact with the Toy Animatronics. But was an eye-witness to see who was the bastard that killed those kids that one night.
Marionette: Gets along with mostly everyone, with Freddy, Goldie, and Balloon Boy being his besties (because Freddy & Goldie are ones Marionette trusts the most, and BB is/was the only other human-like animatronic that resembles a kid).
Toy Freddy: TF may concerted to be Freddy's best friend, but he's unaware that the way he behaves simply annoys Freddy. And he's neutral around Mangle, due to how scary he/she looks & always coming out nowhere when least expected.
Toy Bonnie: Not as friendly as Bonnie, but still gets along with everyone he knows.
Toy Chica: Many had probably made just about everyone be in a relationship and/or have a crush on TC. However, I think it's more believable the other way. Seeing how they made Toy Chica look more girly than the Chicas that came before & after her, she may also have a more girly personality.
And what was one of the more popular girly-girl personality tropes? Being totally boy-crazy and/or be the flirt around the boys. So it's TC that has the crushes on the male animatronics, not the other way around.
Mangle: I see Mangle a bit anti-social around most of the animatronics, with the acception of Foxy because they are both torn apart. And due to the children who keep on taking him/her apart, Mangle's interaction is neutral with BB due to him looking like a kid.
Balloon Boy: Basically he has interacted with everyone, except for Golden Freddy (who he didn't know existed.
The rest pretty much explains a lot (especially the Toy Animatronics hating all of the adult humans).
P.S. Doesn't chart make some kind of pixelated picture/map of something?
Characters belong to Scott Cawthen