I'm guessing that everything remained the same - Cordelia's possession, the Beast, the sun - with the exception of Connor. His part was probably replaced by someone else, maybe even Angel, given the nature of what happened.
If Angel really did win his 'second chance at life' for Darla in the Trials, but she was unable to be cured because she was already living her second chance, Jasmine might have been able to bend that to meaning Angel and Cordelia conceived her as the life he 'won'.
Or, Jasmine might have been taken out of the equation entirely, as a separate entity, and Cordelia's coma was the result of the impact the possession had on her body and whatever was done to her to get rid of the possession. Therefore, there would have been no need for Jasmine to be 'conceived' and Connor was just removed entirely without needing to be replaced by someone else.