  Let $X$ be a compact Hausdorff space and $A$ a Banach algebra. We investigate
amenability properties of the algebra $C(X,A)$ of all $A$-valued continuous
functions. We show that $C(X,A)$ has a bounded approximate diagonal if and only
if $A$ has a bounded approximate diagonal; if $A$ has a compactly central
approximate diagonal (unbounded) then $C(X,A)$ has a compactly approximate
diagonal. Weak amenability of $C(X,A)$ for commutative $A$ is also considered.
