We could have 13 months in a year each with 28 days instead of the current system. that means each month would be exactly 4 weeks so days of the week would land on the same place every year.

To fix the issue with leap years I'd suggest we have 29 days in January and call it January 0, and unlike other days, that would be the day of the week too it would be "day 0" or "zeroday" not sure what to call the month though, might figure that one out in the next shower.