The newest Grapher release added the ability to define a custom fit curve via automation, as well as change the fit curve equation for a custom fit curve. A sample script to do this can be found below.

To run this script:

1. Copy the script below.
2. Open Grapher and turn on the Script Manager by clicking View | Display | Script Manager.
3. Press Ctrl+A to select all of the existing lines in the Script Manager and then press DELETE.
4. Press Ctrl+V to paste it into the Script Manager.
5. Update the lines in the User-defined parameters section.
6. Click the green arrow Start/Resume icon in the Script Manager. 

Sub Main
	
'Initialize Grapher
Dim Grapher As Object
Set Grapher = CreateObject("Grapher.Application")
Grapher.Visible = True

'========================================
'User-defined parameters
'========================================
file$ = "C:\Program Files\Golden Software\Grapher Preview\Samples\Line scatter plot.gpj"

'Fit equations and name
fit1 = "Y = m*x+b"
fitname = "Custom Fit 1"
fit2 = "Y = m*x^2+b"

'Parameters
Dim Array1(1) As String
Array1(0) = "m"
Array1(1) = "b"

'Initial Values
Dim Array2(1) As Double
Array2(0) = 0
Array2(1) = 0

'Minimums
Dim Array3(1) As Double
Array3(0) = -1.79769e+308
Array3(1) = -1.79769e+308

'Maximums
Dim Array4(1) As Double
Array4(0) = 1.79769e+308
Array4(1) = 1.79769e+308
'========================================

'Open an existing file containing a line plot
Set linescatterplotgpj = Grapher.Documents.Open(file$)

'Define object pointer
Set Graph3 = linescatterplotgpj.Shapes.Item(1)
Set LineScatterPlot = Graph3.Plots.Item(1)

'Create the custom fit
Grapher.AddCustomFitDefinition(fitname, fit1, Array1, Array2, Array3, Array4)

'Add the custom fit to the plot
LineScatterPlot.AddFit(grfCustomFit, fitname)
Set Fit = Graph3.Plots.Item(5)

'Change the custom fit equation
Fit.SetCustomEquation(fit2)

End Sub

Updated March 10, 2020