I’m interested in the following certificate programs (aka minors) that my school offers: “Applications of Computing” and “Statistics and Machine Learning”.
I think it depends on what you want to do with your life. I am a political science major, and being that I am interested in attending a PhD program, statistics is very relevant to me. I would recommend “Statistics and Machine Learning.”
Neither of them is better. It depends on your interests and what skills you want to learn.
Although it also depends on the classes. “Applications of Computing” could be basic computer skills classes, IT classes, or programming classes. If they’re more along the lines of programming and data science then that certificate is equally useful as the statistics and machine learning one.
It depends on the courses that make up those two options (or any others). You should ideally look for the strongest quantitative courses you can find to supplement your economics major. Many jobs out there are looking for people in a wide range of majors as long as they have a solid quantitative background, such as a series of advanced calculus courses, several statistics courses, more difficult computing or computational modeling courses, etc. If you decide to go to graduate school, many graduate programs will look for and possibly require a series of quantitative courses as well. Check out the math minor to see how it compares to the statistics minor. Sometimes a math minor will include statistics courses in addition to a series of calculus courses.
As someone who majored in Economics/Finance, I absolutely agree with the above. I’ll also add that if you haven’t already, try a stats class and an applied computers class and see which you like more. Personally, I’d just go with the one you enjoy more. I loved my stats classes, and they naturally led to some good career opportunities just because of my interest. Don’t take classes just because they’re practical 
If the OP had a strong preference, they probably would not be asking for opinions. Applications of Computing does not sound very rigorous. On the other hand, Statistics and Machine Learning is a hot topic in academia and industry right now, and would probably be more financially rewarding.
Well, I don’t think any of these are not rigorous since I’m studying in Princeton but I also think that maybe Machine learning also has something to do with computers.