The Princess and the Frog has... Heck, basically every character with any significance in the bayou is shipping Naveen and Tiana. Ray shows up and quickly creates a She Is Not My Girlfriend moment, and soon he and Louis team up to create a really romantic dance number for the duo. Then Mama Odie shows up and quickly catches on, eventually being the one who marries the couple.
And Lottie willingly passes on her dream to marry a prince when she realizes how much the two love each other. Given how she's rather clueless for most of the movie, this is saying quite a lot.
Virtually all of the castle servants ship Belle and the Beast in Beauty and the Beast. In their case, there was a reason — if the Beast didn't fall in love by a deadline, they were condemned to be teapots and clocks and whatnot for the rest of their lives. Belle happened to be the first girl to show up and fortunately she and the Beast fell for each other. It certainly didn't hurt that they all genuinely liked Belle in her own right, either.
Not to mention Sebastian, who sings to Eric so he will Kiss The Girl. Although it's partly because he knows about Ariel's Deal with the Devil.
Add Grimsby to the list of Eric/Ariel shippers: he not-so-subtly tells Eric that a lot of people are expecting him to marry soon and doesn't that redheaded girl he found on the beach look awfully attractive enough for him to take on a tour around his kingdom?
Grandmother Fa definitely ships Mulan and General Shang.
Mulan (to Shang): Would you like to stay for dinner?
Grandmother Fa: Would you like to stay forever?
The Emperor of China ships Mulan and Shang as well.
Emperor: The flower that blooms in adversity is the most rare and beautiful of all.
Emperor: *suddenly very serious* You don't meet a girl like that every dynasty.
From the sequel, when Shang proposes to Mulan:
Grandmother Fa: I bet he would come before the end of the day.
Father: But I bet he would come before noon.
In Tangled, Cool Horse Maximus clearly ships Rapunzel and Flynn, despite of how started his relationship with the latter. He even gives him a little push. Literally.
Pascal, as well.
Genie in Aladdin ships Aladdin and Jasmine, to the point where he is willing to give up his freedom to see them together:
Genie: Al, no problem. You've still got one wish left. Just say the word and you're a prince again.
Genie: Hey, it's only an eternity of servitude. This is love. Al, you're not gonna find another girl like her in a million years. Believe me, I know. I've looked.
In Wreck-It Ralph, the Laffy Taffy in Sugar Rush are fans of Calhoun and Felix, even forming a heart symbol to frame them in the scene where they serenade the couple.
The soldiers in Calhoun's squad approve of Calhoun x Felix too. When Felix and Calhoun first meet, the marines are glancing at each other and smirking knowingly. Also, in the epilogue, during Calhoun and Felix's wedding, the soldiers all actively ensure they get a happy ending, compared to Calhoun's previous romance.
Max and Roxanne in A Goofy Movie have two shippers. PJ supports Max from the sidelines and does things that could get him in serious trouble with his Abusive Father just to get Max to impress Roxanne (for no compensation) and is repeatedly shown to be happy for Max when things go right in their relationship despite having other reasons to be unhappy. Stacey actively pulls strings in order to get Max and Roxanne together after she notices the look on Roxanne's face, pushes away another girl who tried hitting on Max saying, "Forget it, girl! He's Roxanne's!" and gives Bobby a Death Glare when he makes a comment that suggests Max lied to Roxanne (which he did, but that's not the point).
In Miyazaki's adaptation of Howl's Moving Castle, when the Witch of the Waste realizes just how much Sophie loves Howl, she gives up her own desire to "possess" his heart and gives it to over (figuratively as well as literally). When Sophie's kiss of love breaks Turnip Head's curse and turns him back into the prince, the Witch tells him "It looks like your true love is in love with someone else." Turnip Head himself seems to be in on the Sophie/Howl ship a bit, seeing as he's fine with leaving the two together.
Manolo's father, Carlos, advises Manolo to fight for Maria if he really loves her.
Manolo's grandmother, Anita, gives Manolo key advice on how to woo Maria.
Maria's father, General Posada, prefers that Maria marry Joaquin. His preference is because of Joaquin's reputation as a fighter, thus ensuring the town is safe, and doesn't really take into account Maria's feelings. Although he accepts her marrying Manolo at the end.
By the time Manolo dies in the film, all of the Detention kids are rooting for him and Maria to marry.
La Muerte wagers Manolo and Maria will marry.
Xibalba wagers Joaquin and Maria will marry. Although it should be noted it's less because he thinks they would be good for each other, and more because he made a bet on it.