it's not really necessary to centre point the patch to the joists.
In fact many plasterers do it my way and when doing a whole ceiling if it's straight enough nail/screw an new ceiling over the old using longer screws it obviously prevents dust for months after.
I repaired a patch in my kitchen ceiling by nailing 50x25mm batten to the joists with an overlap of 50mm longer than the hole each end to give area to screw the repair board on to these battens secure it won't fall down then seal the joints with plastering jointing tape then fill/skim with easyplaster [it's a slow setting plaster] from DIY shops or Builders merchant.
WEAR EYESHIELDS WHEN YOU ARE NAILING THE WOOD AND BOARD IN PLACE PLASTER BITS CAN BURN THE EYES MAKING THEM VERY SORE FOR A WHILE. AND A MASK TO PREVENT INHALATION OF DUST. Rub a thin smear of fairy liquid soap on bothsides of the eyeshield lenses then wipe over with tissue this helps to prevent them steaming up especially when wearing a mask.
Bob Whiting
BOB
January 2005