Good question.
Carbon-14 dating is based on the isotope carbon-14, which has a half-life of about 5700 years. This means that every 5700 years, half of your carbon-14 has gone away because of beta decay. Because there is very little to start with, after 5 or 8 half lives, there are increasing problems measuring the beta decay against the background radiation.
To date older materials you simply need isotopes with longer half lives!
On this website: Radiometric Dating: A Christian Perspective by Dr. Roger C. Wiens there is a table of naturally occurring isotopes. These columns are the parent isotope, what it decays into, and the time it takes:
| Samarium-147 | Neodymium-143 | 106 billion |
| Rubidium-87 | Strontium-87 | 48.8 billion |
| Rhenium-187 | Osmium-187 | 42 billion |
| Lutetium-176 | Hafnium-176 | 38 billion |
| Thorium-232 | Lead-208 | 14 billion |
| Uranium-238 | Lead-206 | 4.5 billion |
| Potassium-40 | Argon-40 | 1.26 billion |
| Uranium-235 | Lead-207 | 0.7 billion |
| Beryllium-10 | Boron-10 | 1.52 million |
| Chlorine-36 | Argon-36 | 300000 |
| Carbon-14 | Nitrogen-14 | 5715 |
Many of these are used for dating. Each has its own particular uses and limitations. For example, carbon-14 dating can only be used where there is carbon, so it is good for once-living things (bone, shell, charcoal, peat, etc.).
Check out the website I linked, above, for a lot more good detail.
Thanks for the post. The link is pretty informative. I am amazed that ANYTHING can be dated in the billions-of-years.