I want to comment on some of the discussion that is going on and also say thanks for all of the opinions and insight.
Here are some things I did consider especially since it also involves my son who's 11.
He has his own guns, .22's and enjoys firing them at fairly close distances <50 yds.
He is apprehensive about recoil since he has seen me shoot my 12 ga. and the .303 so I don't want a repeat of a situation years ago with someone and "recoil fear". I know he's not going to want to shoot the .303 and it's too big for him. As for gun safety of a lever action, he has plenty of experience with gun safety and handling.
Yes I can go with a .223 or a similar but this too sometimes gets debated regarding effectiveness, etc., etc. Also I don't see us or myself going often on hunting trips for all different animals and needing a "big" calibre, long distance gun.
My boy is very sensitive toward animals and I have already warned him that killing a deer could be a little upsetting for him, but he still wants to go. Besides wanting to get meat himself, he wants to experience first hand what it's like to hunt for something and then kill it.
So with this in mind and the fact that I always kind of wanted a lever in my collection, all I wanted to know was the calibre's ability on deer at fairly close range since it may get used for this purpose infrequently and maybe used on the odd Coyote instead or at the gravel pit.
I also wanted to know if the Marlin 336BL was any good.
I think those questions have been answered and I thank all those that commented.
I appreciate that you have elaborated here and that you are teaching your son firearms handling and hunting with his own particular sensitivities in mind..... I woudl DEFINITELY take the .30-30 over .223 for deer.... Were I in your shoes I would be looking at a .243 or even .270..... and if you are dead set on a lever I woudl buy a Browning BLR..... but again... that's just me....