Probably not a common use case, but still:
>>> import iris
>>> from cf_units import Unit
>>> u = Unit('days since 1970-01-01', calendar='360_day')
>>> cube = iris.cube.Cube([1], standard_name='time', units=u)
>>> iris.save(cube, 'my.nc')
$ ncdump -h my.nc
netcdf my {
dimensions:
dim0 = 1 ;
variables:
int64 time(dim0) ;
time:standard_name = "time" ;
time:units = "days since 1970-01-01" ;
// global attributes:
:Conventions = "CF-1.5" ;
}