I would think the easiest way to do this, would be to get a general figure of how much sales tax is owed, then a general figure of how much money is going in to each tender type, then take a proportional amount of tax from the respective accounts. Why trouble with trying to figure exactly what numbers match when it doesn't matter anyway?
SubTotal: $20.00 Taxes: $0.50 Total: $20.50 Customer pays $5.00 using Credit Card and $15.50 using Cash. The system does not know which items on the invoice the $5.00 paid for or the $15.50 paid for. All it knows is that Credit Card was X amount and Cash was Y amount.
In a perfect world where all items where taxed and every transaction was paid by only one tender type you could do some reverse calculation to find out the amount of taxes paid by each tender type. But 99.999% of the time that is just not feasible and you will end up with a variance.
What the accounting department needs to do is get in their heads that Taxes have nothing to do with Tender Types.