I have to ask this question because the answer will keep me from going nuts.

My cousin recently preached to one promiscous girl on our street and after that, the girl will not let him be. She's always calling him on the phone requesting that they be friends, that she likes him, etc.
This, my cousin is strongly opposed to, maintaining that he only wanted the girl to repent and not to enter into a relationship with her. Upon all the 'NOs' she gets, the pressure is mounting on him, and this is getting at me.

I'm thinking of answering his phone next time she calls and shouting her down. This is becoming unbearable.

My question is this: How do you politely refuse unwanted love?

Just say "no" in a polite manner and stick to it. Afterall, it's not your phone credit that's being wasted.
Just treat her attempt at dating your cousin as a game or a form of entertainment for you. It's nothing serious.

Have a female friend answer it and say she's his gf.

Honesty is the indeed the best policy. Just be blunt and straight forward. Let her know that your kind gesture should not be misinterpreted for something else.

I hope your cousin is telling you the truth, and there isn't more to this,

But if it is just a case of someone honestly rebuking a sinner, then I think she should understand it was nothing more and move on.

Whether politely or impolitely done,unreciprocated love always hurts.Your cousin's preoccupation should therefore not be guarding her feelings. As said let him be blunt and straight-to-the-point with her,and above all avoid all forms of physical contact.

Thanks all for you comments.

The suggestion of having a female friend answer the call appeals to me. I think it will make her change her mind. I'll do it whenever a female friend is around and the call comes. Meanwhile she'll is still calling. My cousin is regretting giving her his phone number and considering buying another SIM pack.

I don't think I would find the situation so irritating. It's a matter of picking the calls and having fun saying no.