If you listed with only one choice, for example USPS Priority, it is OK to send the item using another shipping method as requested by Buyer. Make sure that Buyer's request comes thru eBay messages to document the fact that the change was initiated by them.
If there is a price difference between listed and requested shipping: if the Buyer-requested shipping method costs more, it's OK to send a PayPal money request to the Buyer to cover the extra cost. If the Buyer-requested shipping method costs less, it's optional (but good for customer relations) for you to refund the difference. Don't forget to take a wide view of the cost difference and act accordingly---for example, if you have to drive a half hour out of your way to send the item by FedEx/UPS, factor that cost into the price difference.
If there is going to be a delivery time difference between listed and requested shipping, be careful. USPS Priority is considered an expedited service by eBay, and generally has a 3-day or less delivery (not incl the day you mail it) to most of USA. If Buyer is requesting a cheaper/slower service from FedEx/UPS, say FedEx Ground or UPS Ground, delivery times are going to be at least as long as Priority and most likely 2-3 days more, depending upon distance. You as ther Seller never want to list an item with an expedited shipping method and on your own change to a slower class of service to save money, BUT, if your Buyer is specifically asking you to do so, it's OK.
