['In essence, they claim that genetic change can happen from generation to generation, but that such changes are always within the context of a species, and that such chages can never result in speciation.']
That is not actually what creationists believe. Creationists definitely believe in speciation, but not change from one kind of animal to another (e.g. chimp to man).
There is plenty of evidence for speciation, which both creationists and evolutionists believe in. Short-haired dogs in tropical climates and long-haired dogs in cold climates can be different species (they may no longer be able to interbreed for various reasons and are therefore considered different species), but they are still both dogs.
The burden of proof is on the evolutionist for anything further than that.