I'm looking to make a light load for youth hunters. around the age of 7 I have 3 different rifles to use I have a savage 30-30 a Mossberg 243 and a marlin 7mm-08.
Any of these rifles modified to fit an "around age 7" shooter?? No matter the recoil level, if the rifle is too big (particularly the stock) they won't be able to use it properly. Also consider the fact that a standard "light" deer rifle, could be close to 10% of the child's body weight. Add a scope and its even more.
How well could you manage a deer rifle that weighed 18lbs with a stock 4-5 inches too long for you???
The loads you are considering will all certainly kill deer, BUT the lighter you go, the more critical it becomes to hit the right spot with a bullet properly built for that spot.
Check you game laws, as well. some places have minimum energy requirements as well as minimum caliber and weight requirements.
One state I know allowed a .25-35 Win for deer, but only the 117gr bullet met all the legal requirements, lighter bullets in that round fell short of the required energy level. (Note, game law minimum energy requirements are NOT the minimum needed to kill a deer, they are a rule of the game)
Also be certain you aren't violating any regs about age, licenses, tags, supervision, etc. These vary widely.
Personally, while I don't think 7 is too young to be introduced to shooting, I think its a bit too young to handle a regular (adult size) rifle, no matter how light the load. Scale the gun to the child (size & weight) or let them grow up a bit more, and you'll have better results, I think.