I took a stab at it, but I'm sure there is a more efficient way of doing this:
Sub Refresh_PivotTables()
' Select L2 Pivots Sheet and update
Sheets("L2 Pivots").Select
ActiveSheet.PivotTables("PivotTable1").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable2").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable3").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable4").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable5").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable6").PivotCache.Refresh
' Select Deskside Pivots shee and update
Sheets("Deskside Pivots").Select
ActiveSheet.PivotTables("PivotTable1").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable2").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable3").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable4").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable5").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable6").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable7").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable8").PivotCache.Refresh
ActiveSheet.PivotTables("PivotTable9").PivotCache.Refresh
End Sub