How can I get power attorney of my cousin at his request if his sister has it now against his will?

If your cousin is legally competent, he can create a new power of attorney document that specifically terminates his previous POA and names you as his new agent. He should also notify anyone who has relied on the earlier document that it is no longer in effect and that his sister no longer has authority to act on his behalf. However, if he is not competent or the current POA has been approved by a court, he will not be able to change agents on his own. Also be aware that becoming an agent for another person opens you up to civil and criminal charges if you mishandle the authority granted to you.