grannies are tricky, it helps to know the type of humor they enjoy in general. was she an abbott and costello fan or a 3 stooges girl?
justice league is good, samurai jack should work, johnny bravo has always been one of my favs, dexter looking back does have alot of made for 9 year olds, jokes that were right up my alley but still good looking back. courage the cowardly dog might somehow be lucky and pass. slapstick is really A GREAT generational gap, i wish shows would stick to that more and leave gross out humor from the slapstick fun. also try some anime, case closed has a good mystery to it. creativity is the key she is watching cartoons to be closer to you and is a bit bored challenge her a bit.
as for 4-8 you need to pick out the looney tunes shorts so that the kids do not get too bored. i would start off with wile coyote, move to foghorn leghorn, then daffy and bugs. also a great one is tom and jerry. general slapstick works wonders for entertainment. also dark wing duck great show, it really gets kids going. plus duck tales is and was a great show. before you start with the disney shows it would help if the kid saw some of the movies first jungle book helps with duck tales helps the kids get the idea of the characters (worked for me).
as they progress classic cartoon network. flintstones, the jetsons, yogi something so they can get involved in stories and characters.
8-12 prime cartoon desire, samurai jack, avatar, johnny bravo, the EDs, gargoyles, justice league, batman and superman TAS, static shock is good, star wars the micro series directed by genndy, the kid should develop a sense for what they like. after that go with what they like.
quick note on the sherlock holmes series: i did like it, maybe i have seen the episodes too much but they got redundant. i like mysteries in general especially ones that can hold me for a bit and holmes did a great job of it. they over complicated things at times and had to cop out due to time and money constraints but overall a good show.