The phrase "a delicate constitution" is correct and usable in written English.
It can be used to describe someone who has a fragile or sensitive physical condition or health.
Example: "Due to her delicate constitution, she must be careful about the foods she eats and the activities she engages in."
Alternatives: "a fragile health" or "a sensitive constitution."
Newsprint has a delicate constitution: fluctuations in temperature and moisture could hasten decay.
The temperature will come as a pleasant surprise and won't shock anyone who has a delicate constitution.
The oyster, you see, has a delicate constitution - "neurotic", Richard calls them - prone to all manner of ailments, susceptible to the warming of water, disturbance, pollution and other modern hazards.
Girls' heightened susceptibility to mass psychogenic illness need not be seen, in other words, as a function of a delicate constitution or a more "hysterical" nature, but of their propensity to talk among themselves about their health.
His willingness to undertake uncomfortable journeys, eat weird foods, and mingle with people very different from himself is far removed from the way I typically think of him as a retired, country gentleman with a delicate constitution.
He was, according to his nephew, "of a delicate constitution having been born earlier than the natural period".
Such advice is mostly nonsense in my experience, though my wife has a more delicate constitution and ate a bit of fresh cod from the fishmonger rather than join me in the salmon.
The medical profession argued that too much thought about maths and money could upset a woman's delicate constitution, disrupting her menstrual cycle and, as Conran pithily puts it, "shrivelling her womb".
There was a tough-guy challenge in the way epic assignments were handed, like untamable horses, to Hollywood men whose gift for intimacy hinted at a delicate emotional constitution.
With my delicate constitution in need of some serious fortification, it's a tough call between fluffy American pancakes (with maple syrup and bacon) or bacon and eggs served on thick, buttery hunks of fresh bread.
Evidently this had started to take its toll on my delicate constitution - by the first week of this year I was nursing a broken ankle, a sprained ankle (the other one), an ear infection (which left me temporarily deaf), and a bout of crabcake-related food poisoning.
