The answer to this question is difficult, because we have to suspend any knowledge or association with Jane Austen's style of writing, her major themes, and the way that all of her works show her typical "endings" and morals to stories. Most of Jane Austen's, if not all of them, end happily, with the main female lead ending up with the right guy. The patient, kind, overlooked females end up with the best men, and are happy. Silly girls either end up with silly men, or learn to not be silly and value good men for their worth. Most of her novels, also, have the charismatic, charming guy that turns out to be evil or corrupt or immoral some way, who, in the end, DOESN'T get what they were striving for (usually money, through the means of a woman with an inheritance). So in order to hypothetically conjecture other possible endings, we have to leave those typical endings of Austen's behind.
There are possible changes to the story. Maybe Wickham and Lydia don't get married; in other Austen novels, similar shallow females like Lydia have been shunned by their lovers and had to live in dishonor with their ruined reputations. Wickham could have gone on to marry someone rich--I've always thought it odd that Wickham, such an obviously greedy character, ran away with the poor Lydia at all. It doesn't really fit; he would have found a wealthy girl to prey upon, and Lydia was not wealthy. So, I could see Wickham leaving Lyddie and marrying a young girl instead. I could also see someone other than Mr. Bingley marrying Jane; she was pretty, kind, and Bingley had been convinced she didn't care for him--Jane could have ended up with someone else, and been happy.
However, both of these events--Jane's marriage to Bingley, and Lydia's to Wickham, serve to restore Mr. Darcy in Elizabeth's good favor. So one has to ask, if Mr. Darcy hadn't coerced Wickham into marrying Lydia (to restore her reputation), and persuaded Bingley that Jane really DID love him, would Elizabeth have changed her opinion of Darcy? Probably not, and if so, Austen would have had to include other eventualities to tweak her opinion of him.
I hope that these thoughts helped; good luck!