Do we ever find out who Coulson's parents are?
There's a S.H.I.E.L.D. file out there on Coulson which lists his father and mother's names as Robert and Julie.
Robert Coulson, Father DECEASED 09-22-1987
Julie Coulson, Mother DECEASED 09-22-1992
However, this source is a bit dubious. It appears to have been present on the S.H.I.E.L.D. Files page of the MCU Wiki at one point in time but has since been removed. I found this one over on the Marvel Cinematic Database's page S.H.I.E.L.D. Files but this wiki is less trustworthy than the MCU Wiki. On top of that the dates for the parents being the same apart from the years is a tad odd.
This is the only source I've found so far for their names but I'm not entirely sure where it has come from so I wouldn't trust it completely as I know there were fan creations of these files going around at one point. I could be wrong and it might be legitimate so I'd be interested in finding out where it came from.