I have two passports, from two different countries. I want to visit another country. I have visa valid for one month on one passport. When I arrive in the country I want to visit, is it possible to ask the border guards to put entry stamps in both passports?
You can travel with two passports, certainly; many dual nationals do so. However, as you seem to require a visa to enter the country you plan to visit, border officials may be unwilling to indicate your arrival on a second document.
If the alternate passport would allow you to enter visa free, why use the one that bears the visa? If a visa is required to use the alternate passport, why would they stamp it without one?
In truth, making such a request may expose you to unwanted scrutiny, or worse.