Conflict is easier for some types of Austenesque novels than others--POV and AU novels should be able to simply tweak the conflict in Austen's original work, though you will of course see those events differently through the lens of your particular character or alternate universe. However, if you're writing a sequel or a variation, you will have to choose a conflict yourself.
A word to variation authors: Many fanfiction writers start writing from a desire to get their favorite characters past the roadblocks more quickly. For instance, you might wish Elizabeth never heard Darcy's initial insult or that Wentworth returned in 1810. However, Jane created those problems for one very good reason: without conflict, there is no plot. Conflict is what drives the story. If you eliminate one difficulty, you must create another.
Since His Good Opinion is told from Darcy's POV, the basic conflict in Pride and Prejudice is expressed differently. I increased the stakes by showing, in detail, how his impression of events is so far from how Elizabeth perceived them. For instance, at the Netherfield Ball when she can barely speak a civil word to him because of his behavior to Wickham, he thinks... well, here. I'll let you read it.
Darcy glanced at his watch one last time. Guests had begun arriving over half an hour ago, and he had purposely delayed his own entrance in order to avoid the Bennet family. For Mrs. Bennet surely saw to it they were among the first to arrive.
He walked through the open doors, and all his good intentions were lost. Elizabeth Bennet stood not ten feet away. Her back was to him, and though Darcy told himself to turn away, to pretend he had not seen her, he could not.
She took his breath away. The delicate fabric of her ball gown revealed more of the lithe lines of her figure than he had previously seen, and the candlelight caught and reflected off the jewels in her hair.
Darcy approached her slowly, gauging his own reaction. Only when he was certain he could maintain his usual reserve did he speak. "Miss Elizabeth?"
She turned, and he wondered if perhaps he had overestimated his own control. Up close, he could see the smooth texture of her creamy skin, and he clenched a fist to keep himself from taking her hand to see if it felt as satiny as it looked.
"Yes, Mr. Darcy?"
He flushed at the question in her voice; how long had he stood without saying a word? "I trust the weather has not dampened your sprits this evening?"
He thought her smile was a little forced, but as he himself struggled to find enjoyment in balls, he did not wonder at it. "You will find, sir, that I rarely allow anything to interfere with my enjoyment."
He bowed and walked away to hide the emotions those words stirred in him. "You will find…" Could this possibly be a hint that she would welcome further attentions from me? Darcy had thought himself immune to her charms, inured against them by the knowledge of her family connections. However, the idea that she would encourage his suit enthralled him, and none of his previous arguments held any weight.
His belief of her affections grows during their stay in Kent, and by the time we get to his first proposal, you might actually feel sympathetic for him, despite the fact that he actually deserves most of Elizabeth's anger.
The conflict in my Colonel Fitzwilliam story revolves around his career as a spy. He's betrayed by someone he trusts, and the resulting disaster makes him unwilling to trust himself. The heroine has to get past his mountain of self-recriminations to prove he's worthy of her trust, and thus, her love.
What kind of monkey wrenches would you throw at our beloved Austen characters?