Coney Weston was recorded in Domesday as "Cunegestuna" and on John Speed's 1610 map as Conyweſton". In 1988 the parish doubled its population by the addition of the pub and its surrounding housing, which was formerly in Barningham.
Coney doesn't refer, as might be thought, to rabbits. It's a Norse word meaning "king's estate" (related to the German könig and Dutch koning).
The Peddar's Way passes through the parish, which also contains several C17th buildings. The church tower fell down in 1690.
In 1843, farm labourer Robert Clarke got hold of a newly-invented material called tinplate and with the help of a piece of wood and some solder created the first tin whistle. He went on to make his fortune manufacturing them in Manchester.
RAF Knettishall was built close to Coney Weston from late 1942 by W&G French and occupied by the USAF 388th Bomb Group from June 1943 until April 1945. Flying B17 (Flying Fortress) aircraft they completed 306 missions, losing almost 180 aircraft to enemy action and other causes. Perhaps their most famous aircraft was called Thomas Paine (named after the famous son of nearby Thetford)…
The 1871 Census for Barningham lists Rebecca Cook (Publican, pub not named, Head/Widow/55/born Coney Weston), which may be the Swan.
Some details from "Suffolk Airfields in WW2" by Graham Smith.