I've got a couple more questions too:

Why is it that BP has so far attempted solutions that only attempt to siphon oil from the well? Why have they not tried closing it?

Is BP's suggestion form a public relations stunt? Or are they really considering the suggestions that are submitted?

OK, back to the original question; here's my answer:
Place three underwater winches in a triangle around the BOP, and anchor them to the Gulf seabed by drilling. Connect the ends of a flat, buoyant, three-pronged structure to the winches with three cables. The center of this structure contains at least one inverted cone (preferably several to make the positioning of the cone easier), which will be pulled down into the broken riser of the BOP. The Bernoulli Principle will help with the positioning of the cone directly into the center of the broken riser. The pressure exerted by the winches will seal shut the riser.

While this does seem possible, there may well be an issues of pressure building up within the well and potentially causing other ruptures in other places, like Santa Barbara in 1969.

Quote:

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In 1969, an oil well six miles (9.7km) off the coast of Santa Barbara, a famed beachside town in California, ruptured.

That well was successfully capped, but the resulting pressure caused five other ruptures along a fault line on the ocean floor. For 11 days, oil spewed out causing an 800 sq mile (2,072 sq km) slick.

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BBC News - How US and Europe differ on offshore drilling

1969_Santa_Barbara_oil_spill

Well it looks like they are going to attempt to seal this leak with what's known as a Top Kill.
BBC News - What is a 'top kill'?