The two children, both eight years old, found the weapon on Friday under a hedge row on the Mourne Road.
An adult noticed them playing with it and immediately removed it from them.
Police attended and confirmed that it was a rechargable stun gun which was then disposed of.
PSNI reminded the public they should never pick up or approach suspicious or unknown objects.
"Fortunately, no one was injured in this incident however the outcome could have been very different," Constable Clements from Craigavon Response said.
"I would strongly advise any member of the public who comes across an unknown object to notify police immediately so that we can ensure their safety.
"I would also ask parents to speak to their children and make them aware that they should not touch any item which they cannot identify."
Anyone seeking advice or who has information on the stun gun is asked to contact PSNI in Lurgan.