This all depends on which traffic your interested in. If you want to decrypt the traffic between your client and the device, then it is possible with a proxy. In fact, it is very similar to how Superfish works. See Lenovo Is Breaking HTTPS Security on its Recent Laptops for an outline of how superfish works.
On the other hand, if you want to decrypt the information your device is sending/receiving from other points, such as what Apple TV might be sending/receiving from Apple, that is much more difficult. I suspect this is likely the traffic you are more interested in.
While the same principal applies - essentially a MiTM (Man in The Middle) attack, you would need to somehow get your device to trust a certificate you own or compromise the private key of the certificate the device uses. This may be easier than it should be or very difficult, depending on how thorough the vendor has been in ensuring adequate security and management of SSL keys. For example, recently it was reported that a well known consumer router and modem manufacturer used the same certificate key on many of their devices, which meant that once you extracted the key from one device, you had access to all the devices using that key. If the manufacturer of your device has implemented similar poor security protection, then there is probably a hole you can exploit. However, finding it is not necessarily trivial. It requires some hacking skills and just the right type of deviant mind to find the weakness. Some people are naturals at this, others not so much.
What you would need to do is get your device to trust a certificate you own and then setup a proxy which has your certificate which will function as a man in the middle. Setting up the proxy is trivial if it is your network i.e. a home network, but getting the device to trust a certificate you have created is much more difficult and does come with some risks i.e. you could corrupt the certificate store on your device and pretty much turn it into a brick and is almost certainly illegal.