The English translation would be "Mi primo tiene once años."
The expression to say how old you are or a material object is in Spanish is "tener ____ años".If you literally want to translate "years old" into Spanish, this would be "años de vejez", but this is nonsense to any Spanish speaker.
You could say "No mucho, primo" (Prima for a female cousin)
i am 41 years old
cien años
años de edad
prima = cousin who is a girl primo = cousin who is a boy
primo Juan
hola primo
De tu primo(a)
You can say "Tengo cinco años".
Tienes quince años.
Tengo diezisiete anos.