You do realize Sivir has the single highest burst out of any AD carry, and is consitantly over 50% in terms of win rate? She's not "sub-par". She's ****ing incredible. The BEST AD to run if you have a heavy AD team.
Okay, onto the actual post. Well, I never liked Trinity on her in the first place. Felt like it delayed real AD for too long, at not as great of a trade off. I like picking up either IE if I'm winning lane hard, or BT if I'm just farming. This allows for some quick AD to make the Q really freakin' hurt early-mid game. After that, you've got some options. If you're split pushing lanes really hard, picking up the Shiv might not be a bad idea to help you push a bit harder. If your team is just poking and all you're doing is chucking Q's, then grabing the other BF item that you didn't get before would make your damage stick even more. After that, I've just been piecing together LW and a GA depending on if I'm getting pressured or not, then just rounding it out with a PD.