You can soften the blow of rejection by referring your client to another vendor.
But just ensure that vendor can deliver what your client is looking for.
And out of courtesy ensure you give the vendor a quick call to explain your situation ‘professionally.’
You should really have a list of vendors, no matter how long you’ve been in business, for this exact scenario.
But if you don’t: At least do some ‘groundwork’ and come up with a ‘list’ of vendors that may be suitable for your client.
That way you are still showing ‘professionalism’ by giving them another option.
Note: If someone has been abusive (in any form) – don’t bother with this step!