Can You Change God's Mind?

Well no.  God is omniscient and knows what is best for us.

 But God was going to destroy Nineveh but the people changed His mind.  Did they really though? (Jonah 3: 10)

And then there's Abraham sweet talking God out of not destroying Sodom.  Or did he?  (Genesis 18: 31-32)

Think deeper.  God always wants what is good for us.  That's His plan from the beginning. God wants us to go to Him, to pray in petition.  He likes us to pray.  Didn't Jesus pray? Sometimes after we pray God will answer with exactly or better than we want.  Sometimes it's wait, not now and sometimes it's no that is not good for you.  We don't change God's mind because this is all part of His plan.