I think the more interesting implication of fossils(not just dinosaurs) revolves around their support for evolution, rather than the 6,000 year old earth stuff. That's targeting the low hanging fruit.
The evidence is clear that all animals have not existed in their current forms since the beginning of time(one religious claim I've seen made). For example, we can say with certainty that cows did not exist in the time of the dinosaurs. One must hold a compromise between the strict interpretation and the reality of science if they want to be taken seriously here. So, god didn't make the dinosaurs and the cows at the same time. We'll chalk that up to poor communication. Then what? Every few million years he changes animals ever so slightly to adapt to their environments when, as living organisms, they are demonstrably capable of doing that on their own? That doesn't sound so convincing either, but that's pretty much what intelligent design is saying. But what it also is, of course, is a further concession that life does change greatly over time, which I know doesn't resonate well with people who don't want to think we share a relatively recent(on a geological time scale) common ancestry with primates.
A more tenable version of ID pseudoscience would go more like "god created life with the function to adapt and evolve based on its environment" rather than god is literally micromanaging the genome every single time a pair on insects bang. Sure, there's no real evidence for it, but at least it acknowledges evolution, while still being able to call itself ID(because god would have designed these functions of life). It might not be ID in spirit, but ID in its current form is dumb as hell anyway so that shouldn't be a problem.
If I were in their boat, I'd honestly just go with "god created the universe and the earth with the specific elements and requirements necessary for life. Life evolved on earth and god recognized that the ape men were going to be the top dogs and began meddling with their affairs after they became the dominant species."
King Percy Bible.