Since no information was available about the size of source range being copied
Following grey areas of the question is assumed as follows
- Since 191 Rows X 68 copy X 3 columns take around 10 minutes only (with you code), the range is about 191 Rows X 15 Columns in size 
- since it has been claimed that code is working Correctly. The Cells of the range (irrespective of their row or column positions) is being copied in column A only (below one and another). Though it contradicts the statement "automate creation of a data table" 
- Since the cells of the ranges are being copied and pasted. In test case formulas are copied only. - So the code below will just replicate what your code is doing with some increased efficiency. As I personally don't prefer to keep calculations, event processing and screen updating off (in normal cases) i haven't added that standard lines. However you may use these standard techniques, depending on the working file condition. Make necessary changes regarding Range etc 
Code takes only 2-3 seconds to complete with  191 Rows X 15 columns X 68 Copies:
Sub test()
Dim SrcWs As Worksheet, DstWs As Worksheet, SrcArr As Variant
Dim Rng As Range, cell As Range, DstArr() As Variant
Dim X As Long, Y As Long, Z As Long, i As Long, LastRow As Long
Dim Chunk60K As Long
Dim tm As Double
tm = Timer
Set SrcWs = ThisWorkbook.Sheets("Input Data")
Set DstWs = ThisWorkbook.Sheets("TrialSheet")
Set Rng = SrcWs.Range("A1:O191")
SrcArr = Rng.Formula
    
LastRow = DstWs.Cells(Rows.Count, "A").End(xlUp).Row + 1
Chunk60K = 0
Z = 1
    For X = 1 To UBound(SrcArr, 1)
    For Y = 1 To UBound(SrcArr, 2)
    For i = 1 To 68
        ReDim Preserve DstArr(1 To Z)
        DstArr(Z) = SrcArr(X, Y)
    
        If Z = 60000 Then  ' To Overcome 65K limit of Application.Transpose
        DstWs.Range("A" & Chunk60K * 60000 + LastRow).Resize(UBound(DstArr, 1), 1).Formula = Application.Transpose(DstArr)
        Chunk60K = Chunk60K + 1
        Z = 1
        ReDim DstArr(1 To 1)
        Debug.Print "Chunk: " & Chunk60K & " Seconds Taken: " & Timer - tm
        Else
        Z = Z + 1
        End If
    
    Next i
    Next Y
    Next X
If Z > 1 Then DstWs.Range("A" & Chunk60K * 60000 + LastRow).Resize(UBound(DstArr, 1), 1).Formula = Application.Transpose(DstArr)
Debug.Print "Seconds Taken: " & Timer - tm
End Sub