"diligently manage" is correct and usable in written English.
You can use it to describe the way in which something is done. For example, "We must diligently manage our resources to ensure our success."
It must be carefully and diligently managed on many different fronts.
And they work -- Alain in New York, Gérard in Geneva -- quietly and diligently managing the family empire.
Nevertheless, Scott will be responsible for finding creative ways for Bryant to have easy scoring chances while also diligently managing his minutes on a roster bereft of talent.
Many of us work diligently to intelligently manage many aspects of our life — how to eat healthier, to work out within our limits, to manage our finances better, and to become professionally fulfilled.
Since then, she has learned to manage the disease, diligently taking her medicine and keeping tabs on her blood sugar.
We manage this process diligently, which may account for some of the differences you appear to have found.
When undertaken correctly, sanitation programs have been shown to be cost-effective and easy to manage, and, if diligently applied, can reduce the risk of microbial or foreign body contamination.
"But we will manage the situation as diligently, as we have done so far".
My friend diligently practiced this philosophy and while he did manage to succeed in avoiding some disappointments by rarely trying new things or taking risks, his whole life was a major disappointment to him because of all that he missed by rationalizing and justifying his fear of loss and making a lifestyle of it.
In addition, VMware, Hewlett-Packard and IBM are all working diligently in the background to find a way to manage the whole enchilada and create a comprehensive virtual data center operating system.
