I was thinking of a set of life forms that originates from neutron superfluid inside a neutron star. So these life forms are not made of atoms but are made entirely of neutrons. How might this life store genetic information and how might it copy this genetic information?
The simplest answer is the Wikipedia article on Robert Forward's Dragon's Egg which has this information culled from the novel.
Around 3000 BC Dragon's Egg cools enough to allow a stable equivalent of "chemistry", in which "compounds" are constructed of nuclei bound by the strong force, rather than of Earth's atoms bound by the electromagnetic force. As the star's chemical processes are about one million times faster than Earth's, self-replicating "molecules" appear shortly and life begins on the star. As the star continues to cool, more complex life evolves, until plant-like organisms appear around 1000 BC. One lineage of these later became the first "animals", the earliest of these stealing seedpods from sessile organisms and some later lineages becoming predators.
There you go, the nuclear equivalent of chemistry and by assuming everything else common to chemistry leading to biochemistry and molecular biology, and by analogy, life. This works for science-fiction, but in the real cosmos who knows?