The Library of Virginia's newspaper collection can provide more information.  I took a quick look at the online collection at virginiachronicle.com and found the following:
a) Petersburg Republican 12-Mar-1819, page 4 col. 2 - An ad offering stud services by a horse named Sir Hal. It says that he won races at Fairfield in 1813 and 1815.
b) Richmond Whig and Commercial Journal 25-Apr-1832 page 3 col. 2 - A story about the resumption of racing at Fairfield after a gap of 17 years.
The older Richmond  papers in their collection that aren't online would be the place to look for earlier mentions of the track.

Racing ads and stories show that racing meets were held in the spring and fall from 1832 to 1860.  I found one mention of a single race held in 1861, by which time the Fairfield course was already a Confederate Army camp.  There were a few races run in the post war period into the 1870's, but not on a regular schedule.  I haven't come across any races in the 1880's or beyond.

The Fairfield course was on land leased from the Fairfield plantation, which was owned by James Talley (no relation).  After his death in 1858, it passed to his son James C. Talley.  He was declared a lunatic and the land was sold off in 1886.  See the sale ad: Richmond Dispatch 03-Jun-1886 page 4 col. 6.  The ad describes the property as a suburb of Richmond.  It must have been annexed into the city sometime after that.

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