I imagine there will be a Pace-Egging Song or two in the DT, that was(is) an Easter custom in the north-west of England. (I have a fine photo of my grandfather in costume, and not very well blacked-up).
That, off-hand, is the only class of songs I can think of in the English folk tradition that are actually about Easter customs, as opposed songs appropriate to the season, of which plenty are mentioned above.
   So do try the DT, I amagine it would be titled either Pace Egg Song or Pace Egging Song.