I have two seeding Copernicia fallaencis that I recently purchased at the Palm Beach Palm & Cycad Society sale. They are now in 7 gallon pots and both have new growth.

Right now I am keeping them in partial (probably 60-70%) shade. When can young copernicias take full sun, and will there growth speed up if placed in full sun?

I'd put them in 4-6hrs direct sun now and water and feed.  They should go into the ground next year, the sooner the better as any delay in the root system growth will delay the growth above ground.  These are full sun palms, but no telling what light conditions they were grown under prior(hence 6hrs direct).  I'd water every 2-3 days and feed with the best time release fertilizer you can buy, florikan nutricote palm formula(8-2-12).  Good luck, these are gorgeous beastly palms, mine is just big enough to walk under.  In 15-20 years you will have a beautiful giant yarey.  

Mine have been growing in full morning sun in the Phoenix area (115 F) summers since their first leaf. I have one in the ground that has had full sun all day since its second leaf and it's fine. Like sonorafans said u have no idea of previous lighting situation. Mine are only 5 gallon size but i can't wait to see how awesome they will be! 

I took a 7 gallon bailey from a heavily wooded lot to an in ground position in my front yard in may 2010, 10hrs sun a day direct sun, no problem.  Today its 12' overall and has a trunk base of ~18-20", boots on.  So I suspect there will be no problem.  Because the fallaensis are difficult ti find, I would go for half day full sun, for now in a smallish(7) container.,

Thank you all for the advice. I have two of them so I am going to move one of them into an area that gets more sun and see what happens.