Dinosaurs Lived with People? Really?!
Teaching in a non-Christian, atheistic country, I have had to think in concise ways for kids to comprehend creation as taught in Genesis. In studying it pretty thoroughly for several years, I see no reason to muddy up the clear reading of the text.
Because secular science has "gotten it wrong" so often, I really feel we need to start simply with what the text of the Bible says and then go out from there. Do we have reason to believe the simple, straightforward reading? There are many sites to get answers for the other scientific doubts that remain. I believe there are very good answers out there. (Here is one.) There are several others. Here are some quick bullet points, first from the Bible and then from science:

1. The Bible says a few times that everything was made in six days. The N.T. (including Jesus) affirms this. The days have the qualifiers "evening and morning" to help us see this clearly.
2. The Bible does not say any animal or anything was created separately from these six days.
3. Therefore man and dinosaurs were created in the same week.
4. Another reason it does not work to say that the days are ages of time: There was no death before sin. According to Gen. 1:29-30, God gave every plant for food (not meat) at the beginning. This was because there was no animal death. (Plant death is different in the Hebrew and in common experience. Plants do not feel conscious pain.) Interestingly, the first animal death is when God sacrifices an animal to make clothes to cover Adam and Eve's sin. We should remember our own sin when we think of death - any animal or human death. More Biblical evidence:
5. Job's "Leviathan" & "Behemoth" (Job 40 & 41) match the description of dinosaurs. No other animals do. No other animal has, for example, "a tail like a cedar". (Job 40:17)
6. The Bible refers to dragons and so does almost EVERY other ancient culture. Why? The only explanation is that there must have been some similar non-mythical animals people really witnessed.

Apart from the Bible we have found: 
1. Dinosaur soft tissue (skin and blood cells). This makes no sense if they were 65 millions years old.
2. Various drawings/artwork and stories of actual encounters with dragons throughout history.
3. Even secular scientists now admit that the majority of the dinosaur fossils we find were buried in massive floods.
4. Various dating methods actually support a young earth much more than an old earth.