I don't put all my trust in carbon dating. I have heard from numerous Christian scientists and some non that it is very unreliable. Any comebacks about how, "their opinion is biased because..." I don't really know how to answer, nor do I want to. You can fight bias with bias but it doesn't really get you anywhere. Yes, distant light, the fossil record, and old Tjikko were created. But I don't believe they are as old as people think.
I must say, you do seem to have a knack for science. I'm not looking to get into a heated argument or try to "convert" you. I'm just trying to have an intelligent discussion.
The specific type of carbon dating that was used to to date that tree is known as Carbon-14 dating. It's almost totally reliable if calibrated properly. Here's a little infograph on how it works:

Almost everything here is completely predictable. The only thing that isn't completely predictable is how much carbon-14 is inside the thing you're trying to date. That's why it's important to provide sufficient evidence that that number is correct within a small margin of error. Which they did. Even if we were wrong we'd have to be randomly off by factors of hundreds of thousands to billions to get the kinds of results that would prove consistently under 6000 years old (In reference to radio-carbon dating, which determined the age of the earth itself. I'm working on calculating how far off we'd have to be to show that the tree is < 6000 yr.). If you have evidence that they were that far off,
please, provide evidence! I'd love to start a scientific revolution.
That old tree was not only carbon-dated but they also used a genetic dating tool, which I'll be honest, I don't know how it works but chances are they make just as few if not fewer assumptions with plenty of evidence to back it up and hence even smaller margins of error. The fact that these two difference measurement techniques provide consistent results only further strengthens the result.
If you have any evidence that cosmological redshifting is inaccurate (which is unlikely since it's purely mathematical and makes no assumptions that we can't calculate accurately) then please provide me with some evidence.