"James likes attention so we'd like to give him a little more of what he craves," it reads.
"If you can be the first to personal message us his correct address, and, as result, we are able to serve him court papers, then we will give you $1000. Discretion is 100 per cent assured, so if you're his 'friend', you can dob him in, with no fear of reprisal."
Bryant said he had been recognised in public since the poster was produced, and the response he had received had been positive.
"A few people have noticed me in the streets and they have given me a high five and one guy even brought me a drink.
"I move to a new area every day so by the time Duco's team get here I'll be in another Airbnb somewhere in this country."
He denied he was on the run from Duco.
"I never admitted I was on the run, I have been on holiday."
Bryant previously told the Herald he wasn't worried about prosecution, and has started a Givealittle page to raise money towards legal fees.
Bryant said his parents, who live on the Hibiscus Coast north of Auckland, had been visited by private investigators looking for him.
Bryant used Facebook's Live feature to stream Parker's fight with Carlos Takam in May, saying the $49 price of the fight was "ridiculous", and issued a challenge to Duco boss Dean Lonergan to sue him.
He is one of eight people identified by a 13-strong combined Duco and Sky team investigating illegal live-streaming.
Duco chief executive Martin Snedden previously told the Herald he was dismissive of Bryant's comments.
"The guy's wrong. In our view it is out-and-out theft, and people are starting to get the message that the risk isn't worth getting involved."
Duco has been contacted by the Herald for comment.
