I have a lot of the same problems you are describing, however I'm still having decent luck getting kids to run during the summer. When I recruit new kids who've never played another sport, getting them to 10-15 mpw is a pretty big accomplishment. Unfortunately, along the way, a number of them develop crappy little lower leg injuries (knee, calf, shin...that type of stuff). If I have them run less, they could avoid the injuries, but would not progress to being any good.
My solution for these newbies (important caveat, I'm going to fully implement this for the first time this year) is as follows.
1. Establish a baseline for what the kids are capable of doing by having them run a short time trial (probably a mile for the newbies).
2. Start every practice with a small amount of running (800m-1 mile)
3. Stage vigorous, general athletic conditioning for the next 20-30 min. (Push up, bear crawl, circuit training, etc).
4. Finish with a small amount of running.
What I just described above would constitute our "quality" days for the early part of the season. The other days would be made up of just easy running where the kids focus on running continuously for longer and longer periods of time.
However, saying "just have the kids do easy running" is also a bit of a trap for coaches of total newbies. For many kids, anything faster than walking pace is hard, so getting them to simply run for 20-30 minutes is not as easy as saying "ok, just run easy, keep it conversational...." So, my solution for those most athletically deficient is to mix walking in with their easy running.
I've had a couple of standards over the last couple of years. Probably the most important one of these is that kids cannot compete in a race until they show me that they can run 20 minutes without stopping. Many kids struggle with this, and despite the fact that we start practice almost 4 weeks before the first meet, do not get to compete in the first meet. I am hoping that by including more non running fitness type activities for the very low level kids, that they will actually progress faster than they would with just running.
HI Coach, keep this thread going. I will keep posting my results as well. I'll even put up sample training for my newbies (a topic which is almost completely ignored on these forums).