what do you mean by adjusting the spec? Are you trying to get Hysys to design a column for a given H2S or CO2 spec? That is about the worst way to go about it. Not only is Hysys very inaccurate when it comes to sweetening, you are asking it to do the impossible.
You should use ProMax for this. And even then, you should use solvers for circulation rate, reboiler duty, lean cooler and lean/rich exchanger. Size your absorber based on the gas flow rate and your regenerator based on your circulation. Your specs should be met after you perform your parametric studies for that unit. Do not use solvers for the sweet gas spec. That will make it difficult for any simulator, let alone Hysys, which not even close to being predictive for sweetening.