Well, consider that, in the Bible, Noah died at the age of 950, a full 350 years after the flood took place. God, meanwhile, created the Heavens and the Earth in seven days. Moses only lived to be 120.
Either some meaning has been lost in the various translations over the ages, or the time spans discussed in biblical references were not meant to be actual time spans as we measure them today, or both.
In geological and archaeological terms, dinosaurs became extinct roughly 64 million years ago, while humans have existed for roughly 500,000 years.
Two arguments from my point of view:
- Dinosaurs were dead long before people ever existed.
- Noah's flood never actually happened.
I don't think that the Bible is meant to be taken literally and so I don't think that there is a problem here.
However, you could also argue that the dinosaurs were taken on the ark and died off afterwards (if you want them on the ark). Or you can argue that they died off sometime between the creation and the flood.
But for me, I don't think the flood ever happened and, if it did, there were no dinosaurs around to take on the ark.