1906
Your serial number indicates that you have a Ithaca crass model double,that was made in 1903.
built in 1908, 104 yrs old
Made in 1901
The date of manufacture of Colt 1903 Hammerless .32 is 1916.(193000-234999)
The serial number indicates Ithaca manufactured your Model 37 in 1956.
For the 03 hammerless .32 model, around 1928
Found a Colt 1903 hammerless with that serial number made in 1917.
There's a list of serial numbers by year at http://ithacagunrepair.com/page5/page23/
For model 03 hammerless .32 produced around 1918
Made in 1916, if 1903 hammerless .32
1934 for the Colt 1903 hammerless .32.
1949