I found a better source on Dunlap's early baseball career than the one used in this post. On October 6, 1887, the Atchison (Kansas) Daily Globe published the same information as Sporting Life (only this time, I could actually read it):
He first played ball at Gloucester, N.J., in 1874. In 1876 he played with the Chester team the fore part of the season, and the latter part with the Quicksteps, of Wilmington, Del., as pitcher. In 1877 he was with the Auburns, of New York, as second baseman, in 1878 with the Hornellsville and Albany clubs, of New York, in 1879 with the Albanys, in 1880 to 1883 with the Cleveland league team...Dunlap is called "the king of second basemen."
Combining the two sources, we now have the following information about Dunlap's pre-major league career:
1874 Gloucester, N.J. (at the tender age of 16)
1875 Greighers (?; based on information passed along to me, I believe this to be the Creighers of Camden, N.J.)
Kleinz of N.J. (playing catcher and ss)
Quicksteps of Wilmington, Del. (pitcher)
1877 Auburns of New York (2nd baseman)
1878 Hornellsville of New York
Also, while I'm thinking about it, the phrase "king of second baseman" appears to have originated in Sporting Life. At the very least, several correspondents of the paper seem to have been using the phrase consistently in the mid to late 1880s. This crowning of Dunlap as king often brought up the question, among other correspondents, of what to call Bid McPhee or Hardy Richardson, implying that they saw these players as superior to Dunlap.