Alliance want Northern Ireland to “lead the way” in the UK and would introduce a bill to Stormont.
But a gay rights campaigner expressed concerned that Alliance backs “such a crazy ban".
LGBT groups have lobbied for legislation to outlaw attempts to change adults or children's sexuality or 'gender identity'.
But religious groups have raised concerns that forms of prayer could be outlawed by a conversion therapy ban, and there have been concerns about how a ban might affect medical treatment of children with gender dysphoria.
In response to the King's Speech, the Alliance Party pledged to bring a private members bill to Stormont to "lead the way for the rest of the UK".
North Down MP Stephen Farry accused Downing Street of "reneging on its commitment to introduce legislation".
Mr Farry told the News Letter that “the government severely failed in its duty to protect the LGBTQ+ community and I can only presume the proposed ban on so-called conversion practices has fallen victim to its contrived culture war ahead of the next general election.
“There is a clear trend in liberal democracies to recognise the harmful nature of this abhorrent practice and to safeguard the vulnerable individuals who undergo this so-called treatment.
"We can no longer delay action to stop the harm it causes.”
However a prominent lesbian academic, who was hounded from her job at Sussex University for expressing views critical of the LGBTQ movement, has welcomed the move.
Professor Kathleen Stock told the News Letter "It's a relief to see that the government has decided not to try to criminalise talking therapies for gender-confused children, who may be pursuing life-altering drugs and surgeries for themselves for the wrong reasons.
The campaigner – who opposes gender identity or 'queer' ideology – hit out at the Alliance Party for supporting a ban that she describes as "crazy".
Stock said "This vulnerable cohort obviously needs proper therapy that explores all options, and not just mindless affirmation from therapists too frightened to say otherwise.
"It's still a worry that the Alliance Party seem hellbent on such a crazy ban in Northern Ireland".
A ban is supported by four of the five main Stormont parties, with the DUP opposing it.