I don't think the timing is going to affect things all that much. If it were me, I would send it to them mutliple times. Send them one now, perhaps follow up with them to see if they received it, and send them one later when it gets closer to the event. Don't be bashful. If I were a coach, I want kids who want to play for me. Let them know of your interest and keep following up with them. Perhaps fill out any online questionaires that are available before you send the letters and that way they will already have two data points on you and it shows your initiative and enthusiasm. Make it happen and it will.