Can I use different initialization vectors (IV) for the same data in AES-CBC?
Yes, this is fine and you should always use a random IV, irregardless of the plaintext.


  The problem is: if I save the same data with the same key several times, I generate different encrypted data.


That's usually a good property to have.

When this property does not hold, it is possible to know when a pair of plaintexts is equal (without knowing the value of plaintexts). That can be a pretty important finding if the set of messages is small (example: something that encrypts "yes" or "no").