The spoof news show poked fun at children dying of leukaemia and a boy in a wheelchair wearing an oxygen mask.
The BCC upheld two complaints out of a total of 20 adjudicated upon last month.
Viewer Bernard Kavanagh claimed that the programme “leered” at children dying with leukaemia.
“Imagine what it is like for the families of terminally ill children in Temple Street and Crumlin children’s hospitals,” he said in a letter to the BCC.
In a sketch about a celebrity charity appeal, Nightlive presenter “Tre-vor Corcoran” describes how his nephew died of leukaemia 10 years before.
“He never got a chance to see me drive Formula Ford at Mondello or caddy for me at Castleknock’s new golf course,” he says.
The BCC agreed the sketch was likely to be offensive to a vast number of viewers.
“Such treatment of a child’s death is inappropriate and the manner and context of a child’s death went beyond acceptable standards,” it said.
“The broadcaster did not exercise due care and the manner and content of the sketch were not appropriate or justifiable.”
In response, RTÉ said it regretted that the joke caused offence and said there was no intention whatsoever to make humour at the expense of the sick child.
Another viewer complained about a scene that shows a young boy in a wheelchair with an oxygen mask and hooked up to a drip. The “weatherman” repeatedly tells the boy to utter a catchphrase but he can only stutter and cough.
The BCC said the humour was in poor taste and was likely to cause undue offence.
In another complaint, it found the humorous content of a Nightlive sketch on motorsport drivers “having a death wish” was reasonable.
Meanwhile, the Complaints Committee of the Advertising Standards Authority for Ireland found 21 advertisements, out of 23 complaints, breached its code on various grounds relating to truthfulness, portrayal of persons and prices.
The ads that drew complaints related to outdoor, television, electronic media and leaflets.