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Could there be a way for a solar system to be very precise, so that the lunar calendar and solar calendar  align?

I know that this is a bit silly, but I want to make a calendar for my world and I'm really worried about having to do leap years and such to ensure continuing accuracy.
Inaccuracy isn't an option, many worlds could simply have a calendar that gradually gets out of line, but the people in this world are very particular about things being easy to understand yet accurate and informative. This would extend to their calendars, I'm sure.
So, I think that the effects of gravity on other planets can affect rotation- I believe the moon is slowly slowing Earth down, right? So, would it be feasable for the sun and planet to influence each other to make sure that years are a whole number of days and that years are a whole number of months?
(This sounds like a stretch, even to me, but might be something about the frequencies of the minor oscillations in orbit plus some other factor- I have limited knowledge of any physics at all, let alone orbital mechanics, so someone smarter than me might know something)
Secondly, could it be possible for this to occur for a planet that is a binary planet? My system is quite lopsided, the centre of the two planet's orbit is only JUST outside of the main planet, but it is still enough to be a binary planet.
~~(if this is impossible, advice on creating a simple yet highly effective calendar for these very fussy people would be nice.)~~

I know that this is a bit silly, but I want to make a calendar for my world and I'm really worried about having to do leap years and such to ensure continuing accuracy.
Inaccuracy isn't an option; many worlds could simply have a calendar that gradually gets out of line, but the people in this world are very particular about things being easy to understand yet accurate and informative. This would extend to their calendars, I'm sure.
So, I think that the effects of gravity on other planets can affect rotation - I believe the moon is slowly slowing Earth down, right? So, would it be feasible for the sun and planet to influence each other to make sure that years are a whole number of days and that years are a whole number of months?
(This sounds like a stretch, even to me, but might be something about the frequencies of the minor oscillations in orbit plus some other factor - I have limited knowledge of any physics at all, let alone orbital mechanics, so someone smarter than me might know something.)
Secondly, could it be possible for this to occur for a planet that is a binary planet? My system is quite lopsided, the centre of the two planets' orbit is only JUST outside of the main planet, but it is still enough to be a binary planet.
(If this is impossible, advice on creating a simple yet highly effective calendar for these very fussy people would be nice.)

orbital-mechanics time-keeping