There is no dogma in the Centerings. Practitioners are free to make any and all adjustments as they see fit. However, I want to suggest three considerations that might be of importance.
First, in order to make them useful to everybody, the Centerings have been written without any reference to deities or belief. However, that does not mean they cannot be used by believers. With slight changes in wording, the names of deities and statements of faith can be inserted into each Centering. Just adding "O God" before a line might be sufficient. I will leave that to you.
The second point relates to the first. Notice that many lines begin with one of three expressions: "I will," "May I," and "Let me." These are interchangeable. I have used them as I saw fit, but there is no reason that a particular one has to be used in a particular case. "I will" is a bit stronger than the other two, but only slightly. Use whatever makes you feel comfortable.
Finally, a word on pronouns (and the necessary changes in verb that accompany them). As the Centerings were designed for solo use, they usually use "I" and "me." However, if you are practicing them with others (see here), you might naturally change these to "we" and "us." The verbs then, also, would need to be changed ("I am" but "We are"). Likewise, a Centering can be "directed" at another person. Instead of "I am staying home," perhaps your sick child is staying home. So instead of "May I," the wording might become "May he" or "May she," etc.
It is recommended that any changes be made in writing, and in the case of practicing with others, copies be made for all Practitioners, to avoid confusion.
See also:
How to Use Your Daily Centerings
Preparing for Your Daily Centerings
A Word on Times
Practicing Your Daily Centerings with Others
The Purpose of Each Practice