The 1871 that GuessL found certainly looks the closest:
RG10/5684 Folio 121 page 6
Ty Cynes, Llansantffraid (Which is the Glyndyfrdwy ED)
Richard Barnard, 59, ag lab, b. Llangwm
Elizabeth, 50. b. Bettws Gwerfyl Goch
Jane, 12,
William, 9
Elizabeth, 4
All children b. Llansantffraid
I noticed that there were quite a few Barnards in the Llangwm district but if he said Lllansantffraid on the 1901, I'm sure this is him rather than the Llangwm one.
Sister Elizabeth is on the 1881 at RG11/5539 Folio 110 Page 10. Still in the broad area. I'm still looking for William
