It probably would be possible to do it with triggers. I wouldn't recommend it, though, and I intentionally didn't mention them.
Triggers are a sort of a "magic" that happens in the background. They are hidden in the database, so easy to forget about, and they tend to interfere with new functionality. If you don't document them thoroughly, the next developer won't have a clue what's happening. Also, there are usually some situations in which triggers don't fire, which may complicate database administration or prevent use of some programming techniques.
There are lots and lots of questions over the internet (on
AskTom, for example) by people who were desperate to resolve their database problem, only to find out there is a forgotten trigger somewhere that they didn't account for.
What you're trying to do with a trigger can be easily achieved by having a single point (say, a method in your project, but even a stored procedure would be better than a trigger) responsible for creating new records in the table. It's a business logic, after all, and it's generally not a good idea to have business logic code scattered all over the place (database triggers and your code, in this case).