His agency, a non-profit society that is mainly funded by the Education Ministry to help schools deal with internet and texting issues, is in the running to become an "approved agency" that will try to resolve complaints quickly, leaving only about 100 cases a year expected to go to the courts.
Mr Cocker said the agency might have to handle perhaps 1000 complaints a year and would be "probably looking at doubling or tripling" its current $1 million annual budget to cope.
The Cabinet paper says the justice sector has committed to staying within existing budget baselines until 2020, so any extra costs for the cyber agency "should be met from existing sources or through reprioritisation".
The proposed new offence of incitement to suicide will apply to all forms of incitement, not just through texting or the internet. It is already a crime to incite someone to suicide if the victim does actually attempt or commit suicide, but the new law will apply even if they don't.
Wellington media lawyer Steven Price said the change would plug a "gap in the law".
"It's been more obviously a gap because you can do it more hurtfully these days, for all the reasons that online harassment multiplies the harm," he said.
Rotorua girl Hayley-Ann Fenton committed suicide in 2009 after receiving threatening texts from the wife of her 27-year-old boyfriend Pelesasa Tiumalu, who was later jailed for having sex with a minor.
The other new offence of using a communications device to cause harm has yet to be drafted. The Law Commission said it should be illegal to send any message that is "grossly offensive", "indecent, obscene or menacing" or "knowingly false", but the Cabinet paper says this needs to be reworded to include material that is posted online but not sent to anyone.
Courts will also get powers to order individuals, internet service providers and social media sites such as Facebook to remove or correct harmful material, apologise, give complainants a right of reply, and disclose the identity of anonymous sources.
Mrs Collins said children under 14 would not be prosecuted for the new criminal offences such as incitement to suicide. "That is where [Police] Youth Aid would normally get involved," she said.
*Read the Cabinet paper and the appendix.
New offences
• Inciting suicide: penalty up to three years' jail.
• Using a communications device to cause harm: three months' jail or $2000 fine.