If your trees are very big and shady, then grass won't grow under them. There are shade grass mixes, but if it's really shady these won't work. Kids don't need lawn, they are usually quite happy in the dirt. (moms usually aren't because of all the mud! :-)

There are tons of plants that grow in shade if you want a kids garden, I suggest posting that in the shade garden forum.

How about making an enormous sandbox? Doesn't need sun, put in ramps, and towers and lots of plastic toys.

Give kids access to a hose and they'll be happy making mudpies.

Thank you for the suggestions, unfortunately I'm afraid leaving it dirt isn't really an option as there is most likely lead in the soil, and the large number of feral cats in the area also rules out a giant sandbox-plus I would really like to see some green.

Goylesgirl,
I have the same problm in our yard. Big, beautiful maples whose roots make digging impossible and who soak up all the nutrients and moisture and sun. We gave up on grass and just put down a huge load of mulch every year. The shredded bark mulches work best because they tend to cling together. I thought wood chips would be nice, but they tend to fly when a child or dog runs through. Our kids love it. We are also able to rake any stray twigs off the grass that does exist and just throw it onto the mulch. The mulch does have to be refreshed each year, because it breaks down and the mud starts to seep through. The more years the mulch has been in place, the better it drains and dries after a rain. Shredded leaves can also be added to the mulched area and helps with the mud problem as well. If you have any questions about how it works for us, e-mail me.
Martha

What did you end up doing? Mulch? Another option? I've got the same problem.
kathryn

I have a similar problem. I have some lawn but it's mostly weeds. I do have some great wild strawberries, I think they are the barren type, that stay lower than the mower and don't care if we walk on them. I would also like to put in a raised bed for the swingset with round gravel because we have drainage problems.

I do recommend hostas, ferns