'Accounting system' is a bit vague - there are typically a number of different modules depending on requirements.
At the 'centre' is the nominal ledger which is tables of nominal accounts, balances and transactions (journals) plus assorted reporting for P&L, balancesheet, cashflow, VAT/Sales Tax etc.
Then you have Sales ledger which is customer records, sales invoices etc which ties back to the nominal ledger to various control accounts. You may also have a separate invoicing module to generate invoices
Next is purchase ledger which similarly ties back to the nominal ledger and again another module to handle purchase order processing
Then stock control which typically links to sales ledger, purchase ledger and nominal plus its own transactions/reports.
And don't forget the banking module - much more complex these days with all the different ways of making and receiving payments.
Also don't forget the auditors - any accounting system must satisfy them that it is reporting accurately.
I'm sure if you look around you will find plenty of examples which cover one module or another in some way but you will struggle to stitch them together into a cohesive whole.
I have many clients where I have written specific modules to tie back to an existing accounting system - for example many invoicing modules only allow you to sell a quantity whereas if you sell glass it is typically sold by area so the user needs to enter glass type, length and width (rather than working it out on a calculator) plus perhaps a cutting charge based the dimensions.
In another case, importing orders/payments from a website.
You will probably be better off investing in an accounting system which you can import/export from and perhaps link to through ODBC (tho' you probably will not be able to make changes to the data through the link)