Sure! It all depends on what you are measuring and what atoms it might contain. Uranium-lead dating (using the decay of Uranium into lead) for example is popular for dating rocks from 2 million up to 2 billion years old (zircon mineral). Also the decay of Potassium into Calcium is a liked method to date rocks with relatively little Calcium compared to Potassium with ages of at least 100.000 years.

Another interesting one is Amino acid dating. Almost all amino acids have an asymmetric carbon atom. So there are two possible ways an amino acid can be oriented. In nature practically all amino acids have a configuration called 'L' and when it decays, it can change to a 'D' configuration. By measuring how many 'D' configurations you have compared to 'L' configurations you could date an organism as well! But this process depends on temperature, humidity... So is more difficult to get a precise age.

Ceramics also have the tendency to capture cosmic radiation in their atomic structure. By heating the sample this energy is released and you can derive how long the sample was exposed to cosmic radiation ==> Age

You also do not always need to measure the object itself to know its age. Many materials in the context of the finding could indicate the age like for example dating ages of stones or found ceramic remains.

I believe these are a few examples of methods that are not affected by our carbon addiction 😃