Concatenate multiple columns of dataframe with a seperating character for Non-null values

I have a data frame like this:

df:
C1   C2  C3
1    4    6
2   NaN   9
3    5   NaN
NaN  7    3

I want to concatenate the 3 columns to a single column with comma as a seperator. But I want the comma(",") only in case of non-null value.

I tried this but this doesn't work for non-null values:

df['New_Col'] = df[['C1','C2','C3']].agg(','.join, axis=1)

This gives me the output:

New_Col
1,4,6
2,,9
3,5,
,7,3

This is my ideal output:

New_Col
1,4,6
2,9
3,5
7,3

Can anyone help me with this?