How would I make a text label update when someone buys in game cash?

The simple answer is easy: Use the ".Changed" event! It's useful for these various things and is used when a value changes (either a "BoolValue", "Color3Value", "IntValue", etc. has changed; It's used when something like your "currency's" value has changed).

Here would be the simple remake of your script:

local P = game.Players.LocalPlayer
local currency = P.stats.Coins --Do not include ".Value" in this because it will return an error!

currency.Changed:Connect(function()
    script.Parent.Text = currency
end) --This function only runs when the value has changed of the "Coins" value

If you have any questions or issues, please contact me. ;)

You could make a Intvalue inside the player to make it so when the player buys the dev product it adds the money to the int value then it goes through the script to the text label you want

game.Players.PlayerAdded:Connect(function(plr)

    local leaderstats = Instance.new("Folder", plr)
    leaderstats.Name = "leaderstats"

    local money = Instance.new("IntValue", leaderstats)
    money.Name = "Money"
end)
local MarketplaceService = game:GetService("MarketplaceService")
local ds = game:GetService("DataStoreService"):GetDataStore("PurchaseHistory")
local pid = 0 --The number of the dev product
local pid1 = 0 --The number of the dev prodcut
MarketplaceService.ProcessReceipt = function(receiptInfo) 

    for i, player in ipairs(game.Players:GetChildren()) do
        if player.userId == receiptInfo.PlayerId then
            if receiptInfo.ProductId == pid then
                player.leaderstats.Money.Value = player.leaderstats.Money.Value + 1000
            elseif receiptInfo.ProductId == pid1 then
                player.leaderstats.Money.Value = player.leaderstats.Money.Value + 6000
            end
        end
    end
    end

If you have any question's let me know.