Simple and straightforward.
My favorite! Please place bills in an envelope, card, or book for discretion.
My preferred method for collecting travel deposits, and a convenient option if you'd like to avoid the hassle of cash.
You have 2 choices here.
1) The easier option:
Send your PayPal payment and classify it as a gift (which waives fees for both parties).
2) The safer option:
I can send you an invoice that accounts for PayPal's 2.9% merchant fee.
While the merchant fee makes the second option marginally more expensive, the benefit is you can file a claim with Paypal if you have issues with the transaction (e.g. you can get a refund if your session never takes place). While I promise I will return your deposit if I cancel our session for reasons that are my fault, classifying the transaction as a payment for a service is a bet-hedging option I like clients to be aware of.
In contrast, the gift option (#1) is more convenient but riskier for you. This is because PayPal treats cash gifts as non-refundable, so once the money is in my hands you have little recourse if I don't follow through. Of course I'd never do that to you.
But then again, every player defects in the last round of a game with a temptation payoff.
Is PayPal discreet?
Yes, as much as possible. The transaction will appear on your bank statement as a payment for a consulting service. Googling the name of this service yields nothing improper.