That's pretty much what in-game club leaderboards are meant for - you create a club with your friends and get to see their times on all the maps you play. Openplanet plugins don't re-implement subscription features, otherwise Nadeo would likely shut down the platform, so for that you'll need Club access.
If you're specifically looking for seeing your friends' times during COTD, you might be interested in https://openplanet.dev/plugin/cotdlivequalifying.