You can post-process the ErrorListPlot output to reverse the vertical axis using ReflectionTransform and modify the ticks:

 Show[MapAt[GeometricTransformation[#, ReflectionTransform[{0, -1}]] &, 
  ErrorListPlot[data], {1}], 
 PlotRange -> {1.8, 2.3}, AxesOrigin -> {Automatic, 2.3}, 
 Ticks -> {Automatic, Charting`FindTicks[{0, 1}, {0, -1}] }]

Alternatively,

Show[ErrorListPlot[data] /. p : _Point | _Line :> 
   GeometricTransformation[p, ReflectionTransform[{0, -1}]], 
 PlotRange -> {1.8, 2.3}, AxesOrigin -> {Automatic, 2.3}, 
 Ticks -> {Automatic, Charting`FindTicks[{0, 1}, {0, -1}] } ]

same picture

You can post-process the ErrorListPlot output to reverse the vertical axis using ReflectionTransform and modify the ticks:

elp = ErrorListPlot[data];
Show[MapAt[GeometricTransformation[#, ReflectionTransform[{0, -1}]] &, elp, {1}], 
 PlotRange -> {1.8, 2.3}, AxesOrigin -> {Automatic, 2.3}, 
 Ticks -> {Automatic, Charting`FindTicks[{0, 1}, {0, -1}] }]

Alternatively,

Show[elp /. p : _Point| _Line :> GeometricTransformation[p, ReflectionTransform[{0, -1}]],
 PlotRange -> {1.8, 2.3}, AxesOrigin -> {Automatic, 2.3}, 
 Ticks -> {Automatic, Charting`FindTicks[{0, 1}, {0, -1}] } ]

same picture

You can post-process the ErrorListPlot output to reverse the vertical axis using ReflectionTransform and modify the ticks:

 Show[MapAt[GeometricTransformation[#, ReflectionTransform[{0, -1}]] &, 
  ErrorListPlot[data], {1}], 
 PlotRange -> {1.8, 2.3}, AxesOrigin -> {Automatic, 2.3}, 
 Ticks -> {Automatic, Charting`FindTicks[{0, 1}, {0, -1}] }]

You can post-process the ErrorListPlot output to reverse the vertical axis using ReflectionTransform and modify the ticks:

 Show[MapAt[GeometricTransformation[#, ReflectionTransform[{0, -1}]] &, 
  ErrorListPlot[data], {1}], 
 PlotRange -> {1.8, 2.3}, AxesOrigin -> {Automatic, 2.3}, 
 Ticks -> {Automatic, Charting`FindTicks[{0, 1}, {0, -1}] }]

Alternatively,

Show[ErrorListPlot[data] /. p : _Point | _Line :> 
   GeometricTransformation[p, ReflectionTransform[{0, -1}]], 
 PlotRange -> {1.8, 2.3}, AxesOrigin -> {Automatic, 2.3}, 
 Ticks -> {Automatic, Charting`FindTicks[{0, 1}, {0, -1}] } ]

same picture