Follow the dress code regardless of age. If cost is a factor, shop consignment stores or Goodwill or something. I shopped consignment and Goodwill both for my 17 yr. old to find him a suit. The way they grow, it makes no sense to pay full price. Little people's clothes do not take up much room so that isn't the issue.
My son , age 11 mostly wore docker type pants and a collared shirt to dinner. Howerer, my friend said her son wore shorts sometimes with no problem. Remember it can be uncomfortably cool in the dining room. I think any pair of tan or black or white pants would do. Don't make yourself crazy. Do what you think is best. I don't have time in my life to worry about what a stranger's child wears to dinner. Relax and have a great vacation.
We just got back from a cruise July 5th -- in the dining room even on formal night the man sitting at the table beside us had on blue jeans. Most of the children that I saw did have on pants -- but one night several teenagers had on blue jeans unbuttoned shirts with a t-shirt under it -sunglasses and a hat
Don't listen to what everyone else is saying...They are not gonna stop you from eating if you are not following "dress code". Sure, adults who wear jeans will look out of place, but as far as kids go, let them wear whatever you feel will be best. Don't go crazy bringing so many different clothes for them to change in...shorts will do just fine. On my cruise (also Miracle 6/12) people were wearing all kinds of stuff...some jeans and some tuxedos. They didnt stop anyone.
On about 5 of my 11 cruises, I have seen familes turned away when the boys, ages 3 and above, were wearing shorts to the dining room. When cruising with my 3 sons, one pair of black dockers would work for the dinner hour, then have them change afterwards. Besides, it teaches them to respect rules. If you are going to the supper clubs, they "require" a coat for the men and I'm sure they would for male children of any age also. The girls will be ok in capris on non-formal nights. As for the jeans on formal nights, I have seen that too on gentlemen from states like Texas, but they were dressy black and looked sharp with their stetsons.