You can ship handguns via UPS or FedEx, but they require you to ship overnight so that will generally be prohibitively expensive. If its within the same state theres no federal LAW preventing you from shipping them a pistol this way, but Fedex and UPS have a private policy that requires they be FFLs, though to be honest the few times I did this there was never any requirement to prove the recipient is an FFL.
01 or better FFLs can ship handguns to other FFLs via USPS priority, all they have to do is fill out a special form to accompany the package. However, this will generally require a transfer fee to be paid on both ends of the transaction, even though its within the same state. You transfer to the pistol to your FFL, your FFL ships to the buyers FFL via USPS, buyers FFL transfers the pistol to the buyer. Two transfer fees and a USPS prority shipping charge.
Basically, theres no cheap way to ship a pistol, either interstate or intrastate. Youre better off doing pistol sales FTF where possible or asking the buyer to cough up the necessary funds to cover the transfer and shipping.