Weights are appropriate throughout the entire season. The issue with distance runners is they don't play football or any sport that lifts so they usually don't know how to do it. That means the first few days need to be focused on form and execution, which can take a lot of time, especially if you need to keep an eye on each kid and help them out. If you can get them on the right track, then I would do weights 2-3 times a week, just basic squats, deadlifts, and some shoulder presses can go a long way. Towards the end of the year taper off so they aren't lifting the week of league, sectionals, etc.
You might get more bang for your buck if you do plyos and bodyweight stuff instead. Take 10 minutes a few times a week to do jump squats, walking lunges, pushups, burpees, side squats, etc. and use the extra time lifting would have taken on more drills, better warm-up/cool-down, or more mileage.