It's likely Coffins by Robert Reed (1992). Anthologized in The Best from Fantasy & Science Fiction A 45th Anniversary Anthology (1994, Ferman & Rusch, eds.), pp.153-164. It begins and ends:
He sits before a projected clerk, confessing his fears.
“You can’t assure my safety. I know this. You can’t tell me that my ship won’t strike a comet or explode on its own. There’s an attrition rate with star travel, isn’t there? It’s got its inherent dangers, and no technology can absolutely guarantee my survival. Am I right?”
The clerk, sculpted from light and designed to nourish confidence, offers an easy smile while nodding. “Your heart,” it offers, “is a chaotic organ, sir. There’s a measurable statistical chance of complete failure sometime during an average thousand-year life span. A tiny chance, but quite real.”
A factory rises on the barren ground. Humming machinery and molds work night and day, producing new citizens by the thousands.
Launchpads shake, mighty rockets driving skyward.
Most are bound for nearby suns, but a few have a more distant and personal goal — capsules bursting open in deep space, shiny figures like dust en route to the ancestor’s homeland.
Multitude and the computer are eventually destroyed in an industrial accident, an experimental plasma drill all but evaporating both of them. And the others, following strict instructions, take what remains to the sea and let the tides take them away. Human faces weep. Human voices sing a light, almost happy song from some vanished world called lo. Then it’s back to work, to life, much to be done and the possibilities without number.