Coherent control techniques are computationally applied to cold (1 mK<T<1 K) and ultracold (T<1 muK) Ne*(3s,3P2)+Ar(1S0) collisions. We show that by using various initial superpositions of the Ne*(3s,3P2) M={-2,-1,0,1,2} Zeeman sublevels it is possible to reduce the Penning ionization and associative ionization cross sections by as much as 4 orders of magnitude. It is also possible to drastically change the ratio of these two processes. The results are based on combining, within the "rotating atom approximation", empirical and ab initio ionization widths.