I did a fair bit of CNC work .... a nesting machine isn't going to do it for you. You are going to need something with a very high Z-axis or will have to create fixtures and manually reposition your work between processes. A CNC lathe might actually be more suitable?
As far as patterns/designs ..... if anyone has created a production pattern for whatever gun you want a stock for ... odds are they are not sharing. It's a lot of work and prototyping.
I ran a Scienci CNC Router for a couple years, long enough to test if it could be used for stock making. the answer was ... sorta. my issues were length - I make long rifles and my max cutting area was only 34"x34"x4" ... so while in theory it could do the job - it would not be large enough for a long gun.
Now, 2 years later, Scienci has added a 48" model and a rotary axis (I think referred to as the A-axis) - still the 4" height issue, but if you could design your setup without a wasteboard allowing the rotary axis to be inline with where the wasteboard would be you could (in theory) do stocks with up to 2-3" drop - still not enough for me. but might be the ticket for modern guns. Have not looked at the $$ lately, but probably get tucked in for about $3500.
I realize the fixturing would be a challenge, As far as size and Z clearance goes, I have a 4x8 table and approx. with 9" of Z clearance depending on cutter length so that should work. A rotary axis would definitely be the way to go.