Since this was never addressed on the show, I think you can be as creative as you'd like to be with your story. Some people have used the "child of a relative" angle, with Jonathan and Martha each telling their families it was from the other side of the family. Others have used the help of an authority figure such as an elderly doctor who signed the paperwork for them. In the comics, as I recall, one continuity had Martha and Jonathan discovering a newborn Clark in the spring after a long, snowy winter, so no one in town had seen Martha in person for months and no one doubted her story when she said she'd been pregnant all winter. In the L&C continuity, since Clark was discovered in May (when presumably Martha would have been out and about), you could have Martha laid up all winter with an illness or injury, and thus be housebound until right before Clark was discovered. That way, there'd be no reason to bring adoption into it at all.
As for whether Smallville residents would gossip about Clark's origins, I think some might, though I doubt anyone would be shocked that a teenager could be unmarried and pregnant. (In fact, it might be an interesting twist if a "fast" Smallville teenage girl left town that winter and everyone in town always just assumed it was secretly her son and that's why the town doctor decided not to ask too many questions.) On the flip side, the gossip might revolve more around the fact that people were so happy for Martha and Jonathan that they'd finally been able to adopt, since everyone felt sorry for their plight.
So I'd say use whatever works for your story -- if you want there to be a scandal, make it a scandal; if you want it to be no big deal, have the neighbors shrug and go about their business.
Kathy
