A rare example exists in "He's Leaving Home" where, upon Manny running away, Bernard struggles to move on despite being a complete bastard to him simply because he cares about him. Taken further in "Manny Come Home" where Bernard is so heartbroken that Manny is leaving that he literally starts dying (and, again, refuses to apologize or show he cares about him).
Manny: Well, I suppose I'll be off since it's over between us... I'll write. Bernard: I won't read it. Manny: W-well I'll call. Bernard: I'll hang up. Manny: [annoyed] Well I'll come and see you! Bernard: [nonchalant] I'll be dead by then.
Later in the same episode has Bernard yell the following at Evan, which is oddly heartwarming in a strange way:
Manny: Bernard! He want's my hair!
Bernard: [to Evan] How dare you! Don't you touch a hair on that boy's head! Have you no respect?! He's mine! Get your own Human Plaything you quartz brained little cream puff!
In the last episode, when Fran falls asleep on the couch, Bernard drapes his coat over her like a blanket.
Another small example, this one from "Hello Sun". Manny makes Fran her favourite dessert, which she's not allowed to eat due to her new Granola Girl lifestyle. Fran tricks Manny into keeping his eyes shut while she digs into the cake. Bernard comes into the room, picks up the empty plate, and puts it down once Manny opens his eyes, taking the rap for Fran. Considering Bernard is cruel and controlling, the fact he's supporting Fran's lie about her new lifestyle is kinda nice.
Another small moment from Bernard appears in "The Entertainer" when he moves to help Mr Slvanski's blind and elderly father walk into the shop. He then does it again with Mr Slvanski's blind and eldery grandfather without so much as a moment of hesitation or word of complaint.