I took the "make them an offer they can't refuse" approach. I made an appointment with the school principal to discuss bringing math contests (AMC 8, MOEMS, Math League) to the school. I came in with enough donations to cover the costs of the contests and enough parent volunteers to run or help teachers run the contests. He solicited for teacher volunteers, and one did volunteer. He decided to be the contact for one of the contests himself. I tool care of all the paper work and fundraising. The teacher just had to oversee the actual contests. She did decide to help with practices as well.
Since then we've expanded the program to the other schools in the district. Parent volunteers run many of the practice sessions we offer before school, and I've set up an online practice program for the high school since the students there are are too busy with other activities to meet weekly as a group. When we don't have a teacher to oversee a contest, I arrange to have another person who can. For example, the rules foe the AMC 8 state, "The AMC 8 must be administered by a teacher or an adult not associated with or related to any of the participants." Most contest rules spell out who is eligible to proctor a contest.
