Is your campaign better served with them as a unique exception, or as part of a community/family/whatever?
If they're an exception, I'd go for the planar traveller route, or perhaps even just leave it unexplained - a mystery that may or may not be resolved as things go on.
If you want a community, I'd probably steal from Zeitgeist: when the Cataclysm occurred, those priests who weren't faithful enough to be Raptured away were transformed into tieflings. They passed on their traits to their offspring, and so in the centuries since several families, some of them very well connected, have sprung up.
Does the player have any idea about the backstory of their PC, family etc, or have they just decided they want to play a tiefling and haven't thought much beyond that yet? I'm not a Dragonlance lore guru, but there doesn't seem to be any obvious lore space for large numbers of tieflings, or tieflings as a widely-known species.
The way i'd do it personally is to say that somewhere in the distant past, one of the PCs evil ancestors made a deal with a fiend of some sort, and the fiend has maintained a connection with the family line ever since. Sort of a family demon, a bit like a guardian angel except ... not. Sometimes the family produces fiend warlocks, and maybe sometimes a child is born that has been tainted by the fiend's proximity and is basically a tiefling. the family could be corrupt nobility or insular pig farmers, anything clannish and insular. And there might be less backlash, angry mobs etc than you'd expect, too. Remember that Raistlin ran around for 6+ books with hourglass-shaped pupils and metallic-looking skin, and I can't remember any of the strangers he met commenting on it. Presumably a tiefling would be treated similarly.
Tieflings have never been explicitly ruled out out Dragonlance, since they didn't exist when the setting was created. Likewise, demons and devils are not explicitly ruled out, but tend not to be a theme the setting deals with. How important is the feel of the setting to your game?
Personally, I would suggest an X-man style mutant (Nightcrawler), or just leave their origin a complete mystery: "I'm an orphan, I don't know who my parents were." The word "tiefling" is never used.
But why does the player want to play a tiefling? If they want a devilish backstory, or a tiefling community, you might have to tell them that's not a direction you see the campaign going in.
You can also punt. Have them wake up with no memories, but people that remember them as a stranger who arrived fairly recently. The PC won't know why they have no memory, why they are so strange, etc... That gives you time to work them into the world in a more meaningful sense. I don't use this approach personally, but I have seen it executed well.
Remember that Raistlin ran around for 6+ books with hourglass-shaped pupils and metallic-looking skin, and I can't remember any of the strangers he met commenting on it. Presumably a tiefling would be treated similarly.
As an adjunct to this, I would add that there is no reason the people of Krynn would associate horns with evil. After all, minotaurs have horns, and they are usually okay. Which could be a problem if your player wants to be a tiefling in order to be dark and edgy. If they are going to associate anything with evil, I would suggest scaly skin.
I can see Otik spitting out his ale when one of these walks into the Inn of the Last Home...
That out of the way, I've seen 4E proposals (when tieflings entered the literature) that tieflings are shards of Chaos, but that doesn't thematically have anything to do with DL1 and would confuse other players as to why that's important.
Perhaps tieflings are the precursor to draconians. The Dark Queen's experiments began with abishai souls into humanoid forms, but they didn't go as expected and aspects of the devils shone through. These experiments were cast aside, perhaps a thousand or so survived, as too unruly and fragile to be capable soldiers. Thanks to the decree of free will for mortals, these new life forms were not beholden to their abishai origins and some chose a less evil path. Because Krynn doesn't have stories of "devils," the appearance may be alien but passed off simply as "I'm from some island that broke off after the Cataclysm." So long as you carry your weight, the folks of Solace might get used to it.