What do I need to change to make this teleportation script work with onClicked instead onTouched?

MouseClick event listeners have a sole parameter, playerWhoClicked. Touched event listeners' parameter, however, is the part which was touched.

The reason it isn't working is because currently part in your script would be the Player who clicked the part. You can fix this problem pretty easily:

EDIT: Somehow, I mistakenly thought that part would be the part touched, instead of the part which touched it. Instead, you should get the player's character:

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local modelname="teleporter1b"
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function onClicked(player)
	local char = player.Character; --// You can get the character just as easily, with some small changes to the function as seen below.
	local h = char:FindFirstChild("Humanoid")
	if h~=nil then
		local teleportfrom=script.Parent.Enabled.Value
		if teleportfrom~=0 then
			local teleportto=script.Parent.Parent:FindFirstChild(modelname)
			if teleportto~=nil then
				local torso = char.Torso
				local location = {teleportto.Position}
				local i = 1

				local x = location[i].x
				local y = location[i].y
				local z = location[i].z

				x = x + math.random(-1, 1)
				z = z + math.random(-1, 1)
				y = y + math.random(2, 3)

				local cf = torso.CFrame
				local lx = 0
				local ly = y
				local lz = 0

				script.Parent.Enabled.Value=0
				teleportto.Enabled.Value=0
				torso.CFrame = CFrame.new(Vector3.new(x,y,z), Vector3.new(lx,ly,lz))
				wait(3)
				script.Parent.Enabled.Value=1
				teleportto.Enabled.Value=1
			else
				print("Could not find teleporter!")
			end
		end
	end
end

script.Parent.ClickDetector.MouseClick:Connect(onClicked)

Also, though yours wasn't too bad, I still urge you to try to always practice correct indentation of blocks.
Hope this helped.