You can use the following code

Unprotect[Zeta]; Zeta[n_] := "Zeta"[n] /; EvenQ[n];

to do what you want on a global level.

You can use the following code

Unprotect[Zeta]; Zeta[n_] := "Zeta"[n] /; EvenQ[n];

to do what you want on a global level. For example

ex = c2*Zeta[2] + c3*Zeta[3] + c4*Zeta[4] + c5*Zeta[5]

returns an expression that prints the same.

Later, when you want the actual values of the even Zetas use this

ex /. {"Zeta"[n_] :> Sum[1/k^n, {k, Infinity}]} // InputForm

which returns

(c2*Pi^2)/6 + (c4*Pi^4)/90 + c3*Zeta[3] + c5*Zeta[5]

You can use the following code

Unprotect[Zeta]; Zeta[n_] := Inactive[Zeta][n] /; EvenQ[n];

to do what you want on a global level.

You can use the following code

Unprotect[Zeta]; Zeta[n_] := "Zeta"[n] /; EvenQ[n];

to do what you want on a global level.