Thanks for your offer which, however, we are not in a position to accept because the date you have required doesn't match the availability of our service. Thanks very much again and looking forward to your next offer.
様々な言表現ができると思うのですが、ビジネスレター風に丁寧に書いてます。
依頼 an offer
~できない、立場にいない be not in a position to ~
希望する日 the date you have required
会わない don't match, doesn't match
Thanks for your offer which, however, we are not in a position to accept because the date you have required doesn't match the availability of our service.
Thanks very much again and looking forward to your next offer.
Thank you for the offer, but I'm afraid I'm not available on that date.
Thank you for the offer, but I'm afraid I'm not available on that date. という表現が、あなたの状況に最も適しています。
Thank you for the offer で、まず依頼への感謝を伝えます。offer は「申し出」「オファー」という意味です。
but I'm afraid は「残念ながら」というニュアンスです。
そして、I'm not available on that date で「その日は都合がつきません」と、はっきりと理由を伝えます。