It is quite hard to sell testing in these days. Clients are always looking for cost savings and it often happens that they are not aware of low quality in the output. How do you deal with that?
If you are building a product for a client, your internal testing / QC work is not subject to negotiations. It is part of the work, part of the price, and there is no reduction in that area. If the client does not want to conduct UAT, that's their choice and risk to accept; however, there's secondary risk on the seller in this scenario. To mitigate the secondary risk, you need to craft your warranty and post production work very carefully where your liability has crystal clear limitations. Your price would need to include a lot of reserves, too. The risk of a bad reputation is there, too, and no amount of contingency can mitigate that. It might be a good contract from which to walk away.
I don't know what kind of work you're doing, but in IT, you could write the contract to say "client will test [list goes here]". When it's time to invoice, your sign off only includes [list goes here]. Make sure your contract clearly defines what you're responsible for during warranty period and that any issues related to items you didn't test are out of scope without an approved change request.
You could also present the client with options for different levels of testing. With this, you explain that your bare minimum testing requirements will be cheap but do not cover x y and z. However, these are your bare minimum testing requirements and cannot be negotiated out.
If you're in engineering, your company may be held accountable for safety and laws.
Why would you want to talk them into testing if they're willing to accept the risk? The answer to that question will be your motivation to persuade the client.
Try searching Google for:
cost of not testing filetype:pdf