Cesare wiping the tears from Vannozza's face and escorting her to Lucrezia's wedding, Rodrigo's decree be damned.
The ending to "Nessuno", if you ignore the shots of the piled-up bodies of Black Plague victims in Naples. The entire extended Borgia family - Rodrigo, Vannozza, Cesare, Juan, Gioffre, Sancia, and even Ursula and Giulia - are gathered together for the birth of Lucrezia's son. Happy, smiling Borgias! No one committing murder or conspiracy for once!
Particularly lovely - at least, to this troper - is when Giulia and Rodrigo walk in, and they and Vannozza are in the same room for the first time. No screaming, ranting, raving, or other nastiness goes on. Instead, the worst that happens is that Vannozza is a bit chilly toward Giulia, which is understandable, and she and Rodrigo reminisce about the birth of their own children and how much they loved them.
In the episode "Paolo", the titular character, Lucrezia's estranged lover and the father of her child, after seeing Lucrezia in Rome for the first time with the promise of seeing her again, is so joyous that he says he has seen Heaven (and might again). His devotion and sincerity is so obvious that the world-wise prostitute who was acting as his tour guide, who sneered at the wealth flaunted by the Borgia family, and who just finished going down on a priest, is moved to tears and gives him a hug. How things work out, though, is more of a Tear Jerker.
Cesare's efforts to reunite Lucrezia with Paolo despite knowing full well that neither his father nor his brother would approve it. And later, he scatters a staring crowd by waving his sword furiously to protect Lucrezia as she weeps over Paolo's dead body.
Vannozza's involvement as well, allowing Lucrezia and Paolo to use her home despite the risk inherent. It's not the first time she's gone against Rodrigo's wishes, and she knows Juan disapproves as well. Add that to the fact that she "knows something about secrets" and loving a man who should be unattainable, and you can see that while she hates to see Lucrezia in this situation, she'll do what she can to make it better.
When Juan brazenly admits to having murdered Paolo in cold blood, Rodrigo's reaction is to charge him straight across the dinner table, enraged, and Juan hurriedly reminds him that Rodrigo's own plans for Lucrezia would have demanded it in any case. While Rodrigo can't berate or discipline Juan for the murder without barefaced hypocrisy, it's obvious that he really, really wants to, and the scene makes it clear that while he's fine with the assassination of political enemies, his own sons killing innocents does NOT fly with him, at least not on an emotional level.
Rodrigo and Vannozza in "The Purge", after Rodrigo survives the poisoning. Rodrigo talks about how, if he weren't Pope and had the choice, he'd want to retire to his vineyard in Spain with Vannozza. It's bittersweet, because it will never happen, but it's nice seeing the bit of humanity Rodrigo has left.
Rodrigo: You make us feel safe, Vannozza.
Your mileage may vary very heavily on this one, but Lucrezia and Cesare consummating their incest in season 3 episode 3 is the first time we've seen both of them genuinely happy in a long time, and while they know they're crossing a line, the scene itself is very tender, and if they weren't brother and sister it would be one of the most gentle and loving sex scenes in the series.
And then we have Micheletto murdering the King of Naples in 3x05. Why? Because he wouldn't allow Lucrezia to bring Giovanni with her into the city. When you take into account how Micheletto always dotes on the baby, and how he tells Lucrezia that he would 'bind his children to him with steel' if he had any of his own, plus the fact that murdering him has no political benefit for Lucrezia (her husband isn't even next in line to the throne!) and it's clear that one of the show's most ruthless sociopaths has a soft spot for the child.
Becomes more obvious in the next episode when Micheletto takes Giovanni from his nurse so he can hand-deliver him to Lucrezia himself.
3x09 Rodrigo and Cesare finally reconcile, Rodrigo forgives Cesare for murdering Juan, and they pledge to trust each other and work together to protect their family. It's made all the more heartwarming by the fact that it follows a huge Tearjerker where Rodrigo finally reveals all his self-loathing and anger over everything he's done and keeps doing.