Pour the pineapple juice and rum into a large bowl. Add the coconut flavouring and lime juice.
Whisk the icing sugar into the juice until dissolved.
Whisk in the cream and keep whisking until soft peaks form.
Taste to see if you need more coconut flavouring or a squeeze more lime juice. Keep in mind that frozen desserts always have a milder flavor and are less sweet once frozen.
Spoon and smooth the ice cream into an airtight container and freeze.