Obviously, George R. Martin draws heavily from medieval history in writing GoT; Lancasters become Lannisters, along with many other elements of pre-Tudor power struggles...but is our lovable onion knight based on any actual historical figures?
There are a number of historical counterparts which can be associated with Davos. The most prominent comparison is likely that of Thomas Cromwell.
1) Both men were of common birth; with Davos coming from flea bottom, and Cromwell being the son of a blacksmith from Surrey.
2) Both men were largely disliked by the landed gentry
3) Both men acted as advisers to a strong willed king and spoke their views openly regarding issues facing their monarch.
Davos's story is that of upward mobility; a quintessential example of the self made man. A rather good character analysis can be found in this article by Steven Attewell over at (RACE FOR THE IRON THRONE)
Davos's character seems to act more as a literary contrast to Littlefinger and Bronn than fill the role of a historical equivalent. Davos represents morality, Bronn is amoral, and Littlefinger immoral.
Davos doesn't crave growth or glory and only want to do the best for his king and his family, Bronn will take advantage of the opportunities when they arise, and Littlefinger actively craves more power.