It once and a while happens that a program that says it requires Windows 3.1 on the box is actually a 3.0 application. Check the expected windows version number in the executable, if it is set to 3.1 then it simply is not a 3.0 application and 3.0 will refuse to run it. If it says 3.0, then just try it on 3.0 and see if it runs. If it starts to load on 3.0 but complains about missing Microsoft DLLs, then the easiest way to get those is to install Visual Basic 3.0 (it bundles all 3.0 update DLLs, like the common dialog DLL).
If you are looking to make it run in 3.0 8088 real mode, you can forget it. Of all of the native 3.0 application programs I have seen, I think I have only come across two that will do that.