The plan is contained in a Law Commission report which also recommends laws to tackle online harassment.
The laws would make it a criminal offence to encourage someone to commit suicide, to post "intimate images" online without the subject's consent and to "maliciously impersonate" someone on social media such as Facebook and Twitter.
The commission has completed an initial year-long examination of gaps in laws and regulations that have emerged with the public's increasing use of social media and consumption of online news.
In an "issues paper", the commission said the internet and associated technologies "create novel ways of causing harm through speech abuses - and create numerous challenges for those seeking to enforce the law or obtain remedies".
While there were already laws which could be used against cyber bullies, "a distressed victim or a young person may not wish to give evidence in court" and civil action was often beyond their financial reach.
One alternative was a tribunal operating at a lower level than the court system but which could administer "speedy, efficient and relatively cheap justice".
The tribunal would hear complaints and potentially make orders for compensation, an apology or a correction. It could also issue a "take down" order.
Another proposal was for an independent commissioner to whom victims could turn.
Netsafe executive director Martin Cocker welcomed the proposals. "It gets to the heart of the problem with all of this which is that it's very easy to offend against somebody in these ways but very difficult for people to take action to remedy that."
Prof John Burrows, of the Law Commission, said the proposed law against "maliciously impersonating another person" would not block satirical accounts.
"There's always room for satire, there's always room for good-natured imitation but we're talking about things that cause genuine harm to other people ..."
In the other major strand of the commission's work it has proposed sweeping changes to regulation of the news media with a single, independent watchdog that would replace the Press Council and Broadcasting Standards Authority.
News media could only continue to enjoy privileges such as access to closed court proceedings and exemptions from some legislation - including the Privacy and Defamation Acts - if they submitted to the proposed body.
