A good place to see some of their responses to C14 dating and the refutation of them is the Talk Origins Index of Creationist Claims. Starting at CC310 is where you'll find the relevant entries.
Regarding the speed of light, if you can possibly imagine the silliness of it, they invoke something called "tired light", their name for the idea that the speed of light has slowed down such that what appears to be far away on the theory that light's speed is constant, is really far closer and therefore in accord with a young Earth.
Clearly, god is such a devious character that he emplaced photons en route to Earth so that it appears that there are stars and galaxies spread all across the Universe. Obviously, this is to test the faith of scientists to weed out non-believers. Well, at least that is the implications if we are to believe the nonsense from the young Earth creationists.
When I was a kid and questioned how fossils came to be.. I was told Satan did it. It didn't make sense to me then and even less so now.
For a funny take on this: http://www.youtube.com/watch?v=_9Wx6-c8VSo
Based off conversations I've had .. They only seem to pay attention to the carbon (C14) dating and how inaccurate it is to date things beyond 60,000 years. They totally disregard the other types of radioactive dating.
The funny thing is, no one uses C14 to date things beyond 60tya because of the inherent limitations of the method. So arguing that the method is inaccurate after that point says nothing of use.
It's also true that the C14 method needs calibrating. Which has been done. But they can use C14's need for calibration to try to argue that the method is inherently bogus.
Mineral dating (most famously U-238->Lead 206, but there are MANY others) doesn't have any of these problems and can date into the billions of years quite easily. Which is why the less clever creationists ignore it, and the more clever ones have to come up with additional bullshit arguments against it.
Radiometric dating is inherently flawed, and god created the light from the stars reaching earth when he created the world.
There is a quantum creation model that suggests the universe was created in a very small space, and then stretched rapidly to it's current size. That stretching caused a time dilation and through some rather creative inverting led to an old looking cosmos, but a young earth. Somehow the early days on earth actually equated to billions of years by modern standards while the later days of the (expanding) cosmos covered billions of years by modern standards. I can't remember the exact name of the theory or the author, but if you run across it then check it out - although it still leads to the oomphalos fallacy of last Thursdayism.
That seems like an interesting attack for the creationist. However, I don't know how it would hold up against astrophysics, etc.
Well, you gotta give 'em koodos for epistemological plasticity. :D
It holds up fine if you're willing to ignore facts & logic. Otherwise? Not so much at all.