Radiometric dating works by calculating the age of rocks using a radioisotope's half-life and the relative amounts of that radioisotope and its byproducts. The YECs claim that radiometric dating is unreliable due to either contamination or changes in the half-life.
On pages 24 and 25 of WEIT, Coyne utterly demolishes this claim. He starts off with three basics that provide more than enough evidence by themselves:
"Since the different radioisotopes in a rock decay in different ways, they wouldn't give consistent dates if decay rates changed. Moreover, the half-lives of isotopes don't change when scientists subject them to extreme temperatures and pressures in the laboratory. And when radiometric dates can be checked against dates from the historical record, as with the carbon-14 method, they invariably agree."
I especially like that second one: environmental conditions (e.g. the ones before or during the supposed flood) don't change the decay rates of radioactive isotopes used in these dating methods. It's hard to take the YEC argument seriously when all of the evidence points in the opposite direction. (And a technique called isochron dating limits any potential problems with the method even further.)
Then Coyne recounts an ingenious method for independently confirming the accuracy of radiometric dating. Certain corals were dated to 380 million years ago. Cornell University's John Wells took advantage of the fact that friction from the tides is gradually slowing the earth's rotation to confirm this date. We know from the rate of slowing that 380 million years ago, each year would have 396 days, each 22 hours long. Corals produce growth rings daily and annually, and Wells counted those rings to find that his corals had experienced about 400 21.9-hour days per year – remarkably close to what was predicted by radiometric dating.
This elegant independent confirmation leaves me in awe of the ingenuity of scientists. These are not people who blindly follow the principles that have already been set up. They perform countless experiments that could potentially falsify the existing paradigms. But in most cases, this one included, these tests add new support for what we already know. This is in stark contrast to young earthers, who cling to whatever scraps of supposed evidence they can find and come up with wild, unsupported hypotheses to keep believing what they want to believe.