Can we call the coefficient of an algebraic expression a constant? Can we call the coefficient of an algebraic expression a constant?
For example, in $6y$ is the $6$ a constant?
 A: The number $6$  is fixed and , in the expression $6y$ it is constant, in the sense that we can chose any value for $y$ , but the expression indicate that this value is always multiplied by the constant number $6$. Obviously the expression $6y$ is not a constant if we can chose different values of $y$.
A: For the polynomial  $$ P(x) = a_0+a_1x+a_2x^2+...a_nx^n $$the constants,$$ a_0, a_1,a_2,...,a_n$$ are called coefficients.
They are constants but using the word constant may apply  only to $a_0$
A: According to the Clark's Dictionary of Analysis, Calculus, and Differential Equations, a constant is 

A quantity that does not vary. A symbol that represents the same quantity
  throughout a discussion.

And, according to the Krantz's Dictionary of Algebra, Arithmetic, and Trigonometry,

Given an equation in a variable $x$, any part of the equation that is independent of $x$ is a constant term.

So, in these senses: yes, we can say that the coefficients of algebraic expressions are constants.
But note that some constants are not coefficients and "variable coefficients" appear in some contexts.
