What is the adjective for a person that has cancer? For example, cancerous individual, cancerous child, or something else?
The adjective cancerous usually modifies cells, growth, tumor, etc.
It is better to use a prepositional phrase with cancer which post-modifies the noun.
A person (diagnosed) with cancer
Or you could use cancer patient which means:
a person who is receiving medical treatment for a malignant growth or tumour: 'an increase in the number of cancer patients'
We never use the adjective cancerous to refer to a person suffering from cancer. If you do so, you may cause people great offense as well as emotional pain.
If you wish to refer to people who have cancer, you can refer to them as cancer patients, as noted in another answer here. You can also refer to people with cancer as cancer sufferers or people with cancer.
One reason that you might offend them is because "cancerous person" is often used metaphorically to describe a person regularly causing negative effects to others around them i.e. that person is a metaphorical cancer.
In English it is common to use the term "cancer patient" as stated already. The following is not a real answer, as much as a suggestion: in Greek, someone suffering from cancer is called carcinopathés (noun, a person suffering from cancer). I think the addition of a term such as carcinopath or canceropath in the English vocabulary wouldn't go amiss.
There is no single word adjective you can come up with that won't range from being offensive, to extremely offensive and whose use won't mark you as a weirdo with no social sense.
Nevertheless, if my life somehow depended on coming up with one, I would make my answer "becancered", taking advantage of the "be-" morphological formation to denote "afflicted with", "surrounded with", "loaded with", "stricken" and such.
Somehow it has a small softening effect, placing a separation between the subject and the disease. There is a certain slight nuance in "cancered" in that to be "cancered" is in some sense, to be identified as being one with the cancer, to be inseparable from it, or the degradation of health which the progression of cancer causes. The "be-" prefix re-frames the cancer as some external affliction which in some metaphoric sense drapes the individual and can be shed, or something that the subject has (like a "bespectacled" person is someone who is wearing glasses, and something "bejeweled" is covered with jewels).
This possibly may have to do with "be + word + ed" plausibly deriving from a noun sense of word. In "becancered", "cancer" refers to the noun "cancer", and not to cancer as a verb, unlike in "cancered", where the derivation is ambiguous; there is a verb sense which means "degraded by the progressive action of cancer" and not simply "having cancer".
Most sources I can find online tell me "cancerous" is grammatically correct for both a growth and a person, as meaning "relating to or affected with cancer".
Though if I may, I find this expression very repulsive. It might be because I played online games too much, but I think that referring to a "patient with cancer" or a "cancer patient" sounds way better than a "cancerous/cancered(?) patient".