Hi,
As a DM, I always include custom content to my adventures. Custom magic items that will end up in the hands of the players, custom spell that they will discover, custom feat for warriors of a particular region, etc... In this way, I tend to give my world the game-content needed. And I would invite you to do the same, as long as the roleplay needs it, don't hesitate to implement new stuff (sparingly). It's a part of the DM's work. However, some knowledge about how to write stuff is necessary, there is some sort of nomenclature about how is written a feat, a spell, etc...
Don't worry about having all your players asking you for their special artifact, you don't have to always say yes. If they are wise enough, they'll understand that it would be non-sense. Otherwise, you'll have to be creative.
In your situation, your should write by yourself the dragonbone armor. Decide if it needs to be an artifact or an ordinary magical armor, but even in the second option, don't hesitate to write custom magical proprierties to fit with what your player wrote about (custom special material ?). The item hasn't to be exaclty what expected, because there's always that legend facts distortion.
I'll moderate my argument if the backstory of that character has absolutely nothing to do with the adventure. If it goes out of nowhere, you could ask your player to tone his background to better integrate the group and the adventure (most of the time it won't need much effort, and minor changes). Alternatively, you could integrate his item in your adventure's storyline. Secondary quest, or secondary goal. That NPC could know about the armor localisation, but he won't tell the character before they do this of that.
I would conclude by saying that characters with backstories are extra work, but it could be a source of inspiration (if sufficiently written).
I hope my point of view can be useful to you in any way.
Deimvune