How can one refuse a spouse's request without hurting their feelings?

Refuse with gentle words, give an honest reason and, if possible, offer an alternative — because how you refuse matters as much as the decision itself.
Allah teaches: if you must turn away from them because you have nothing yet to give, speak to them a gentle word (al-Isra' 17:28), and a kind word is better than giving followed by hurt (al-Baqarah 2:263). For example: "I understand you really want that holiday; this month we cannot afford it, could we save a little each month for the school holidays?" is better than "stop being so demanding". Do not refuse through sarcasm, silence or ignoring messages. If the request is an obligatory right, such as maintenance or one's turn on the rota, it cannot be refused at will. The spouse who is refused should also accept "no" maturely. See Emotional communication.