If you aren't seeing weekly (or daily) challenges, I found a way to trigger them without uninstalling. You can basically skip the phone ahead day by day to make them trigger at midnight.
1) Close Temple Run 2.
2) Go to Settings -> time + language -> date+time and turn "Set Date and time automatically" to OFF.
3) Now set the time to 11:59PM of the current day.
4) Load up the app and wait in game for midnight to pass.
5) If daily and weekly challenges do not appear. Then repeat steps 1-4 with the new current day.
6) Once the challenges are available, turn the option "Set Date and time automatically" back to ON and continue playing on the current day.
So if it doesn't work the first time, let's say on the 1st, then repeat the steps on the 2nd, the 3rd, the 4th, etc by changing the time over and over until the challenges reset correctly. It only took me two time changes to get both daily and weekly challenges to register.