Is it possible to integrate an AI CoPilot on existing planes?
If an "AI Co-pilot" existed, it could likely be integrated on existing airplanes with an auto-pilot system.

Since your question is a little vague, I'm going to take a stab at some your hidden assumptions and go from there. I'm also making the assumption that you're talking about the enroute phase of flight, and leaving the taxiing, take-off and landing in the hands of the human pilot.

At the risk of (extreme) oversimplifying, an AI system is essentially something that takes in a lot of data, analyzes it (through different algorithms) and outputs data that can then be used to do something. 

I'm going to assume that the AI algorithm is supervised and has been trained on a bunch of existing data, and it has been figured out what data is important to make high-probability inferences.

In-flight, there are multiple sources of data that could be fed to the AI algorithm for it to make probabilistic inferences on what it should do.  These data sources are things like:


Engine monitors (my EDM 700 I think logs 60 data points/second on things such as cylinder head temperature, exhaust gas temperature, RPM, location, power setting, etc.)
GPS Receivers (3D position)
AHRS (attitude information)
ADS-B (Traffic and Weather)
On-board Weather Radar
XM Satellite Weather


(As an aside, SavvyAnalysis already does a bit of this type of analysis using the data from your engine monitor).

So, provided that your "AI Co-pilot" has been properly trained in advance on the same type of data that you are able get from your airplane while in-flight, your AI Co-pilot could ingest the data, and output signals to the auto-pilot which would then fly the airplane. The autopilot controller is simply sending information to a particular servo for a particular control surface (aileron, elevator, etc.) and if your AI Co-pilot can output the same signal, then it could control the servos the same as the autopilot.

One of the (many) difficulties lies in designing the system to safely handle things that it hasn't seen in the training data.

But to answer your question, it wouldn't require the design of a new aircraft, but rather a new autopilot control system.

EDIT: Extra thoughts

After thinking about your question some more, I was thinking why you might want an AI Co-pilot? I'm thinking the answer to that might would be for it to either make decisions for you that you are unaware you should be making or to help you make better decisions.  There is existing software that does something like this, called Xavion, which continually figures out where you should land if your engine quits based on the current location and performance of your airplane. It's not hooked up to an autopilot, but it wouldn't be too far of a stretch to think that sometime in the future, something like this could be a part of the autopilot controller.


  Furthermore, Xavion is constantly running engine-out flight
  simulations behind-the-scenes as you fly. The app imagines an engine
  failure every single second, and it checks how your plane would do in
  a power-off glides to every runway at every airport in gliding range.
  
  For each of these simulated engine failures, Xavion estimates the
  likelihood of a successful landing based on the runway’s length,
  width, proximity to the aircraft, and glide path from your current
  location down to the threshold of that runway. When Xavion has found
  the runway that it believes is most likely to result in a safe
  engine-out landing, it builds a series of hoops from your current
  location to that runway—spiraling, circling, or extending as needed in
  order for the hoops to follow a constant descent angle that your
  airplane should be able to sustain without power.


When you start to think of something like this, you can start to imagine analyzing real-time weather data and having the system make (or help make) a decision to divert or land based on your performance and experience. However, this is all something that would happen in the auto-pilot controller, so retrofitting it to an airplane with an existing autopilot would be more of a software upgrade than a hardware redesign.

UPDATE:

Wired had a good article on this on 3/28/2017. It talks about all the different sources of data that could be used to make an AI learn about the airplane, figure out where the holes are in the data and who could fill them.  An interesting place for data that I didn't think about (because it's not data generated in flight), is maintenance and service logs.

Particularly relevant to the intent (I think) of your question might be this passage:


  Elsewhere, researchers are working to ensure AI can help pilots manage
  crises as they arise. At University College London, a team led by
  Haitham Baomar and Peter Bentley is developing a new autopilot system
  that learns how to manage emergencies by watching how well-trained
  pilots do so, and then behaving as they do in similar circumstances.
  
  “We want to increase safety by trying to tackle the human-error factor
  that might be caused by stress, information overload, and sometimes a
  lack of sufficient and up-to-date training,” Baomar says. “Modern
  autopilots, unfortunately, can’t handle challenging flight conditions
  such as severe weather conditions or system failures.”