SABL

Before I would try any type of putty, I would try a narrow strip of neoprene and a hose clamp. Wrap the joint with the neoprene ( a heater hose section which has been split lengthwise) and secure in place with the hose clamp.... like a common automotive application. Not the best way to do a fix but it might do the trick.

The proper way is to do as Carsey recommended... but unless you are adept at "sweating" pipes you could dig yourself a deeper hole.... and completely de-solder the joint. Also, like Davis55 stated, if there is even a drop of water in the area of the joint you will not get the heat required to get the solder to melt..... let alone to get it to flow into the joint.

With any luck, the nonleaking pipe will still contain some water and there is little chance of de-soldering that fitting and the leaking side will be empty. If the leaking side is not empty, you may be able to disconnect it downstream of the fitting and allow it to drain so you can resolder the leak.

Good luck,
SABL