I'm not going to find our speaker even though my sister asked me to.
Why not find the speaker for your sister?
I don't feel like doing it.
It's good to help out your siblings when you can, so I think you should help your sister find the speaker. It would be rude to not help her out just because you don't feel like it.
I'm tired and I don't feel like it. Find it yourself.
They're not my sister but they are yours. Siblings should be willing to do small favors for one another in order to keep their relationship healthy. If she can't rely on you than your relationship might worsen.