Ok, I am reading the excursions and most of them have an age limit.  Now when we went on a cruise before, I remember a grandpa that went on the excursion with his family to watch the grandkids.  This was a snorkel excursion.  He stayed on the sailboat while the parents snorkeled.  So my question is, the excursions that have excursions that have age limits on them, can my 4 year old still go if an adult stays with him and we pay for each person?

Almost certainly -- if you get a private excursion.  They tend to be very flexible.

Maybe not if you do the Carnival excursion.

It depends on the excursion.  With some the mode of travel may not be suitable or allowed for young children, and there may not be an area for an adult to wait with a child.  What excursion were you thinking about if you don't mind me asking?