International Reply Coupons "IRC" were created for that purpose. However, I'm not certain if USPS continues to sell them. Check with your local Post Office.
Airmail postage would be GBP 1.70 or GBP 2.55 (the latter if weight is over 20 grams)
Worst case, email me your address and your cousin's address and I'll send him the SASE.