It doesn't actually need to fit exactly what I imagine from reading the books. The Patronus just adapts beautifully to a world that's not its home.
Since I collected most of these quotes anyway (and intended to get the rest when I will reread DH), here is what we know of "Happy Memories":
"[You conjure a Patronus] with an incantation, which will work only if you are concentrating, with all your might, on a single, very happy memory." (PA 12, Lupin teaching Harry)
"[Harry ...] settled on the moment when he had first ridden a broomstick.
'Right,' he said, trying to recall as exactly as possible the wonderful soaring sensation in his stomach." (PA 12, practicing.)
"Harry thought hard, and decided his feelings when Gryffindor had won the House Championship last year definitely qualified as very happy […]
'Ready,' said Harry, trying hard to fill his head with happy thoughts about Gryffindor winning [...]" (PA 12, practicing.)
"He racked his brains. A really, really happy memory … one that he could turn into a good, strong Patronus …
The moment when he'd first found out he was a wizard, and would be leaving the Dursleys for Hogwarts! If that wasn't a happy memory, he didn't know what was … concentrating very hard on how he had felt when he'd realised he'd be leaving Privet Drive, Harry got to his feet and faced the packing case once more." (PA 12, practicing. First successful attempt with a Bogart pretending to be a Dementor.)
"He didn't stop to think. Plunging a hand down the neck of his robes, he whipped out his wand and roared, 'Expecto patronum!'" (PA 13. Harry doesn't need a memory. Playing Quidditch is happiness, and he is about to catch the Snitch.)
"'Hermione, think of something happy!' Harry yelled […]
I'm going to live with my godfather. I'm leaving the Dursleys.
He forced himself to think of Sirius, and only Sirius, and began to chant: Expecto patronum! Expecto patronum!" (PA 20. Still depending on a recent conversation, but more an expectation than a memory. Hermione tries and fails.)
"And then it hit him – he understood. He hadn't seen his father – he had seen himself –
Harry flung himself out from behind the bush and pulled out his wand.
'EXPECTO PATRONUM!' he yelled." (PA 21. Time traveling Harry does what he watched himself doing.)
"He summoned the happiest thought he could, concentrated with all his might on the thought of getting out of the maze and celebrating with Ron and Hermione, raised his wand and cried, 'Expecto patronum!'" (GF 31, Third Task.)
"He was never going to see Ron and Hermione again –
And their faces burst clearly into his mind as he fought for breath.
'EXPECTO PATRONUM!'" (OP 1, Harry had nearly been overwhelmed.)
"You've got to think of something happy." (OP 27, Harry teaching Dumbledore's Army.)
"Harry raised his wand, looked directly at Umbridge and imagined her being sacked." (OP 31, examination.)
"It was of Ron and Hermione that he thought as he whispered. ‘Expecto patronum!" (DH 28.)
"’That’s right, Harry ... come on, think of something happy ...’
‘Something happy?’ he said, his voice cracked.
‘We’re all still here,’ she whispered, ‘we’re still fighting. Come on, now ...’" (DH 32, Luna Lovegood helping out.)
HG