Here's what I've come up with and please bear with me.
The map is from 1873.
First of all, Locust Valley is shown as the terminus of the branch. Locust Valley was opened in 1869.
Oyster bay was built in 1889.
Therefore the map is sometime between 1869 and 1889. Using the other posters' comments about the connection to Eastport, etc. would make this era about right.
Now, let's fine tune it some more:
Along the main line, BOTH Suffok Station and Central Islip are listed as stops. Suffolk Station was closed in 1873 with the opening of Central Islip the same year.
As they are both shown as stops, it would appear that CI had just opened and Suffolk Station had not yet been removed.
Hence, 1873.
Does the reasoning sound OK?
Dave Keller