After a hearing in early September, Justice Mary Peters released the decision today.
She said the appeal against sentence was allowed.
She quashed the jail time and replaced it with four months' home detention.
Justice Peters also ordered Parkin to complete 400 hours of community work.
The appeal decision stated Parkin challenged the sentence on the grounds it was "manifestly excessive".
He argued it was excessive in terms of the length, and the fact that Judge Ronayne had "erred" in refusing to hand down a sentence of home detention.
"Ultimately, the Judge said he had decided against home detention because the offending was serious; because of its aggravating features – premeditation, the vulnerability of and harm to the complainant, the fact that the offending had occurred twice, the abuse of trust and the degree of violation," said Justice Peters.
The law states that the court must have "regard to the desirability of keeping offenders in the community" and that "precludes the imposition of a sentence of imprisonment unless the relevant purposes and principles of sentencing cannot otherwise be achieved".
Parkin's lawyer submitted that Judge Ronayne had erred by "placing too much weight
on the need for denunciation and deterrence".
He had also focused too heavily Parkin's continued denial of the complainant's account, and placed insufficient weight on the isolated and historic nature of the offending.
He submitted the judge was wrong to consider the appellant in need of rehabilitation, given the 37 year gap between the alleged offending and his arrest.
Justice Peters said a sentencing judge must evaluate "all relevant purposes and principles of sentencing in deciding whether to impose a sentence of imprisonment or home
detention".
"Of the reasons the judge gave for preferring imprisonment to home detention ... none appear to us to call for a sentence of imprisonment," she ruled.
"Moreover, and as (Parkin's lawyer) submitted, in making this critical decision, the judge has not taken into account the lapse in time since the offending and what that signifies.
"We consider this omission to be a material error."
Justice Peters said there was "no apparent need to deter" Parkin from further offending or to protect the community from him.
"And as we have said, a sentence of home detention is equally capable of meeting all of the (Sentencing Act) purposes in any event.
"Any sexual offending against a child is serious, but this was relatively fleeting and isolated.
"There is nothing in the nature of this offending, as opposed to other sexual offending against a child, that would seem to require a sentence of imprisonment."
Justice Peters said the Court of Appeal also needed to bear in mind the need to impose the least restrictive outcome appropriate in the circumstances.
"The appellant appears to be a good candidate for home detention," she said.
"Taking all of these matters into account, we consider a sentence of home detention will be sufficient to meet the purposes and principles of sentencing relevant in this case and we shall quash the sentences of imprisonment accordingly."
"Our order quashing the judge's sentences and imposing the sentences of home detention is to take effect as soon as practicable and, in any event, by
4pm, October 5, 2018."
