Welcome and thanks for your question!
The answer is it depends on whether the customer is purchasing a service or a product with the deal coupon.
If the customer is purchasing a deal for a specific product or service subject to tax (e.g. a manicure), then sales tax
is only due on the amount the customer purchased the deal for.
If the customer is purchasing a deal for a stated value (e.g. $50 value purchased for $25), then sales tax is due on the full amount of the taxable products sold/services rendered.
The amount of money that your salon receives from the website is not relevant in the determination of how much sales tax the customer should pay.
New York issued a fairly in-depth Techinical Memorandum
on the subject that you may wish to consult for further reading. Also, here's a nice summary guide
to taxable and nontaxable salon services.
Please let me know if you need clarification or have any further questions on this subject. If you are satisfied with this service, please accept this answer with a positive rating. Have a wonderful evening and good luck with your new business!