Is there any way to recover this? Can I change it without knowing my current password?
No. You cannot recover the contents of the keychain without the password. There is no way to reset the password retaining the keychain data.
If you want to access a login keychain after changing user's password, the keychain will still be accessible using the old password.
If the problem is reappearing password prompt after a login password change, you can delete and recreate the keychain, but the original data is non-recoverable.