My kids and I have actually quite enjoyed trips to the cemetery. I was inspired by Starr Hailey Campbell's book The Adventures of James: A Trip to the Cemetery. I read the book with my kids and then we tried it. She suggests you:
›Take a picnic
›Make file cards on who you are looking for. Have a prize for finding the right stone.
›Take a cemetery kit with treats, water, cleaning supplies, etc.
›Tell them about the person as you are traveling, cleaning headstones.
We put together a cemetery kit with CheeseIts, one of my grandmother's favorite treats. (You know, everything with kids goes well when there is food involved.) We sat and cleaned her stone to make a rubbing and I told them all about her. And we took a large sheet of paper so we could make a rubbing-genealogy chart of sorts of the ancestors we had in that cemetery. The kids really had quite a good time and have even enjoyed going back.
If you take them to a Library or Family History Center you might try to let them try to find something new. Or you might give them an easy find, something you already know about but know might peak their interest. The 1930’s census is very detailed, and a good place to start. If you ever take a group of kids who don't know much about their family--like a scout troop or such, the 1930 census is close enough to know who to look for (Usually grandparents or so), and can spark curiosity about their lives. With your family you might also try a Scavenger Hunt—Let them explore and find the sources for what you already know. My kids quite enjoy the trip. They really get excited when we find something new. We usually take them out to dinner and make it a fun evening. It probably doesn't hurt that we let them play on the internet so we can finish up when they start to get bored. But even though we sometimes give in a little at the end, but it is well worth it when they look forward to going again the next time.