The tongue-in-cheek gift was in addition to a white cot cover and sheet hand-embroidered by nuns in Miriam's home village in Spain.
Speaking on his regular Call Clegg phone-in on LBC 97.3 radio, Mr Clegg said: "Miriam and I sent a letter with a gift just yesterday to Kensington Palace.
"The gift comes in two parts. We found a beautiful cot cover and cot sheet which is hand-embroidered in a convent in the village where Miriam comes from in Spain, where I was for a few days a few days ago.
"We have thrown in with the gift a large bag of our favourite coffee, because as parents of young boys we know you need coffee when you are coping with little boys."
Labour leader Ed Miliband's gift was said to be a traditional gift for a first-born son.
The tree is three years old and nearly ready for planting out, and already has some fruit growing on it. It was sourced from local community groups the Brent Eleven Streets residents association and the London Orchard Project.