If you want something to start running and then keep running forever, then you'd need to use an always-on task rather than a scheduled task. However, if that's what you meant -- a good way to periodically restart them would then to use the API to tell the system to restart them at a particular time, via a scheduled task. While scheduled tasks can only be scheduled hourly or daily, you could get one to perform an action by scheduling it daily, and then checking the day of the week at the start of the script and exiting early if it's not (say) Sunday:
import sys
from datetime import datetime
# Check if the current day is Sunday (Sunday is represented by 6 in Python)
if datetime.today().weekday() != 6:
sys.exit()