COGS, when you pay taxes, is the cost of items stocked in inventory and sold. Not something you buy for a job and do not stock. You should, in the chart of accounts create a new account, type = COGS but it is titled Cost of Sales, (COS) and use that for job expenses.
A deposit is a company liability, you took money and the company owes the customer something in return. So in the chart of account create a new account, type is liability and title it customer deposits. Then create a service type item that links to the customer deposit account and use it on a sales receipt to record getting the deposit.
When you invoice for the job, as the last line select the customer deposit item set the qty to a negative one, (-1) and enter the amount of the deposit.
Yes the deposit is income when the invoice is prepared. On the P&L income is reduced by expenses.
