An alternative to rejection sampling (as described in FrankW's answer) is to use a scaling algorithm, that takes into account an answer of [7,8] as if it was another coin flipping.
There is a very detailed explanation at mathforum.org, including the algorithm (its NextBit() would be flipping your fair coin).
The case for throwing a dice with a fair coin (sampling 2 → 6) is easier than the generic algorithm. You just take a failure (7 or 8) as another coin input and perform two more flips.
