I am selling my car to an individual who wishes to purchase the car from me for 30k in cash. I asked for a check instead but they stated they only have cash. What sort of paperwork would I need to submit to deposit this cash into my checking account. I am selling the car at a loss so there are no capital gains on this sale.
You don't need any paperwork other than a deposit slip to deposit the cash into the account. The BANK will need to fill out a form to help the Government detect money laundering, counterfeiting and other crimes. If you aren't doing any of these things you have nothing to worry about.
This is not going to trigger any tax liability unless you report it on your tax returns as a capital gain or other type of income.
The one thing you DON'T want to do is split it into several smaller deposits that are just below the reporting limit. That is called "structuring" and will trigger some alarm bells you don't want rung.
Your main risk is being tricked by the buyer. There are not many (legal) reasons why someone has 30k in cash but cannot use bank account to pay you, so chances are the money is illegal. That is not really your problem, unless the police thinks you should have reasonably known that, or the money is fake.
If the government comes after you (chances are they have bigger fish to fry), you should be able to prove how you came into posession of it - which should be easy, the car ownership was in your name, and is now transferred. Having a copy of the sale contract might be helpful.
It is legal to sell your car for cash; just be careful that you don't get tricked or robbed.