Roman Numerals are meant for numbers not words. However, since January is the first month the year simply writing "I" followed by the day and year would suffice.
Example: January 1st, 2013 - I/I/MMXIII
January 20th, 2009 can be written as XX.I.MMIX in Roman numerals.
I/V
The date January 8, 2001, is written as VIII.I.MMCI in Roman numerals.
January 1st, 1993 in Roman numerals is written as I.I.MCMXCIII.
I/i/mmxi
XXIX-January
January 20th, 2009 can be written as XX.I.MMIX in Roman numerals.
I/V
January would be represented with an I. You would write it as I-XI.
The date January 8, 2001, is written as VIII.I.MMCI in Roman numerals.
January 1st, 1993 in Roman numerals is written as I.I.MCMXCIII.
I/i/mmxi
I.III.MCMXCIV
It is: I-I-MMXII
January 13th 2000 can also be written as 01-13-2000 and in Roman numerals that would be I.XIII.MM
1977 January 1 is written as I.I.MCMLXXVII in Roman numerals.
I ix mcmxciv