Gear/approach to legimitately mining (not buying) a single Bitcoin Background
I have a relative who has been trying to get into Bitcoin mining. He accidentally installed malware onto his home PC twice, thinking it was a mining tool. He understands mathematics but is not well versed with modern technology, PCs, etc.
Question
What sort of hardware/software/etc would I purchase if I want to have a standalone device sitting (quietly) in the corner of my office that would have a reasonable expectation (95%+ CI) of earning a single coin within, ideally, 6 months? The power/hydro bill isn't a problem, as I'll be paying it. It's to my understanding that I need to consider ASIC/FPGA-based boards to be remotely competitive.
Goal
My goal is to pre-mine a single coin, give him the box as a birthday present, and have a cron job add the coin to his wallet at a set date. I think it'd make his day (day he always felt lucky).
Additional info
How do I help him legitimately cash-out his single bitcoin, so that the bulk of the face-value is cashed out, and he has a receipt he can file properly at tax time?
Bitcoins aren't mined individually; they're awarded to miners who discover a block.  This process is like a race that restarts every ten minutes when a new block is mined (the miner gets a block reward plus transaction fees).

In order to have a shot at winning these races, mining operations use expensive arrays of custom hardware.  So, without that, you would have a pretty slim chance of discovering a block before one of them did.