FuncToList[f_,n_]:=CoefficientList[Series[f[x],{x,0,n}],x];
R[g_,alpha_]:=Function[x,Evaluate[alpha g[g[x/alpha]]]];

f2[x_]:=1+c2 x^2+c4 x^4;
U=FuncToList[R[f2,a],4];
Equations={U[[1]]==1,U[[3]]==c2,U[[5]]==c4};

NSolve[ {U[[1]]==1,U[[3]]==c2,U[[5]]==c4},{c2,c4,a}]

