Your job pays "under the table"?? what does this mean? should the internal revenue service investigate you?
If i were a bank, i would not give you a loan, either. you apparently, are dodging paying taxes.

My suggestion: get an honest job, pay taxes, pay social security,like the rest of us and then, ask for loan money to buy a car.

You are who you are. a new car loan is not yours, without deserving it.

Get the creditials, then get the loan!

You better hope uncle Sam doesn't subscribe to answerbag,he could subpoena AB's files to find out who you are.
What do you mean by excellent credit? according to equifax or the fact you don't have any loan history?no history can be worse than bad credit.

Just because you have a job off the books does not mean that you are breaking the law. It's if you don't show income to the IRS that can be considered illegal (though there is even dispute if taxes are constitutional or not, but lets not go there). What you have to do is go to an accountant and have them help you file as an independant contractor (or something like that) and then you have income to show the banks. Chances are that you will have to pay taxes though.

print your own payslips

There are drawbacks to working under the table. Ya, you seemingly make more because there are no taxes and such. But should you ever get hurt on the job, bet your life that your employer will deny he ever knew you and you'll be financially screwed with doctor bills as L&I won't give you a dime.