"Carbon-dating doesn't work. It's been shown to be inaccurate for objects older than 30,000 years."

Tell me, would you say that a 25m tape measure "doesn't work" because it can't measure distances longer than 25 metres? It still works within that range, doesn't it?

Carbon dating is only used within its range, just as a tape measure is only used for objects within its range. For older objects, radioisotopes with much longer half-lives (such as uranium) are used for dating purposes, just as you would use a different kind of device to measure very long distances (eg- to the Moon).

For those of you who wish to adopt a more conciliatory approach, it is noteworthy that there is a famous line in the Bible about a day being as a thousand years to God, thus implying that timescales in the Bible are not meant to be taken literally (quite frankly, none of it was meant to be taken literally, but if you're out to convince someone without browbeating him, a certain level of pandering can sometimes be useful). In general, there is far more Christian flexibility on the issue of the age of the universe than there is on the issue of evolution itself, so instead of resigning yourself to a rhetorical battle against someone who digs in his heels and closes his mind to evidence, you should keep in mind that it is possible to convince a Christian of the validity of these concepts if you work at it.

Fallacy watch:

• Straw-man fallacy (pretends that carbon-dating is used for objects dating back millions or billions of years, when in fact it is not).

Recommended further reading:

• TalkOrigins article: Radiometric Dating and the Geologic Time scale
  
• ASA article: Radiometric Dating: a Christian Perspective