What would be a suitable material, in terms of durability and cost, for a children's desk?
For a piece of furniture that's destined for the lifetime of abuses that children can inflict upon it, I view it from two different schools of thought.
The first school says that since you expect the piece to be beaten up, painted, and generally neglected, you will want to make it out of a material that maximizes durability while minimizing cost.
For my money, this wood is usually southern pine or douglas fir. I built my workbench out of southern pine for this reason. Spruce is also a very strong material for it's cost and weight, though it dents very easily.
The second school says that because of the abuse you expect, you should go ahead and spend your money on a hardwood that will take the abuse in stride. Something that will not chip easily, something that holds a nice edge without denting, and something that doesn't show scratches just by looking at it.
For example, the bed frames my father built for my brother and I as kids were made of red oak, and they experienced their fair share of abuse from two energetic boys. Both are now relegated to our hunting cabin and have been transformed into bunk beds that my brother and I use to this day, over a quarter of a century later. They remain sturdy because they were built well out of a stout material.
In this case, a good hard maple or red oak would be perfect. Both are fairly inexpensive (in my area, at least - your mileage may vary), and using them for something that the Queen won't use is perfectly acceptable.
For painting, poplar is a good choice since it takes paint well. If I recall correctly, alkyd-based paint is best for poplar. It's a fairly soft wood, so expect some denting.
There is a tendency to want to cheapen the things we give to children because of the though that the kids won't appreciate them and that they'll abuse them. I find that this depends on how the kid(s) is (are) raised. Giving them something nice and instilling in them the idea that they are responsible for keeping it nice, I think, is one of the best things you can do as an adult.
Too often these days we/make buy crappy furniture out of cheap materials under the expectation that it will get used until it falls apart. I say, "no!" The truly environmentally-friendly way to make furniture is to make so well that it will outlast you and your children.