Lots of ways to try to get at this:
Topographic Position Index http://www.jennessent.com/downloads/tpi-poster-tnc_18x22.pdf
Elevation residuals (DEM minus a smoothed version of DEM)
Local maxima (Focal Statistics with "Maximum".
All of these will give a resulting raster. Threshold the output raster appropriately (should be fairly standard on peat lands), then convert those raster zones of interest to points or generate centroids of those zones. All of it can be automated in Model Builder or Python.
In ArcMap, assuming you have access to the Spatial Analyst extension, use the Raster Calculator tool and enter: "DEM" - FocalStatistics("DEM", NbrCircle(5, "MAP"), "MEAN", "DATA"). Where "DEM" is your elevation raster and 5 in this case being a 5 m radius on which to generate mean values. This equation will subtract the mean raster value of a 5m radius around each cell, from the actual value of that cell. This gives a relative slope position for each cell where negative values are lower than the surrounding average and positive are higher than the surrounding average. Tweak the radius to generalize at different scales.