how would you make Laurel likeable?
1) Make her a hero
"You Catch 'Em I Cook 'em" Show her being a heroic lawyer in the courtroom, make it cool, if necessary steal some of the best bits from Law & Order/Boston Legal/Judge Judy or what have you.
2) Give her a personal life
We used to spend a lot of time in Laurel's apartment, but... we still don't know who this chick is, what she does when she's not addicted to something. We know about Dig's home life, we know about Felicity's personal life from her mumbling, we know all about Thea and Roy. Who the heck is Laurel Lance outside of her relationship with the rest of the main cast? Perhaps making her a workout-aholic as many recovering addicts are makes sense, perhaps a love interest in a trainer, or something?
3) Have her kick butt physically
Let her beat up some folks with Bamford, and honestly, people will get on board pretty quickly. Most people that read the comics could care less about what Dinah Lance does when her mask is not on.
4) Show why Sara died.
Perhaps there was some secret reason that Sara was in town the night she died, reveal that, helps take some edge off the 'Laurel killed Sara' feeling some folks have.
5) Deliver on the previous seasons
If you can tie what Laurel's been through during previous seasons into a neat package, it can almost make it seem like she was a better character then than she was. Delivering on the addiction, on the lawyering, tying those together and funneling it all into a place where you say "of course the ex-addict lawyer would end up being Black Canary, it was inevitable." If you can pull that off, Laurel would become my favorite character.