John:
I've identified approximately 1800 courses built before 1910 (the majority of these being private clubs). If it helps your analysis, there were probably around 1400 courses built before 1901. My guess is that there may be another 100 or 200 from the period from 1901 to 1910 that have slipped through the historical records. By 1940 approximately 7,000 courses had been constructed, although many of these had disappeared by that time.
The first real boom in US golf course construction occurred between 1895 and 1900.
Sources include the Harpers Reports, the Annual Guides, a plethora of books on various subjects, the early golf magazines, listings of works from every known architect from the era and this website (particularly information provided by Tom MacWood).
Hope that helps,
Sven