'daily arguments' is correct and usable in written English.
You could use it when referring to a regular argument or disagreement between two or more people. For example, "The teenagers in the family had daily arguments about who was doing the most chores".
Here at TechCrunch there's a daily argument in the office, on Yammer and even on the blog about the supremacy of the iPhone versus the Google-Voice-goodness of Android phones.
When I see it in the morning, I remember that you raised three boys, and I try to channel the force of your love, as my own son and I have our daily argument over pants or shorts.
Doing more to help the less affluent with parenting, even if this requires "taking on the Daily Mail argument about the nanny state".
Todd Bowles, a safety then and now an assistant with Miami, listened daily to impassioned arguments, but never considered crossing.
The Democratic establishment in 2005 was under assault from online activists who demanded that the party modernize its message and appeal to voters in all 50 states; now conservative blogs like The Next Right and The New Majority are making the exact same argument daily.
Whether the fiscal cliff is a real one or a manufactured one, and if real, whether it can be circumvented without lasting damage to vital welfare programs -- all that remains momentarily unresolved and as such, the legitimate subject of a daily deluge of argument.
Although one of Kahneman's arguments, demonstrated daily in all of our lives, is that we're most likely to believe evidence that supports our existing beliefs, whether it's good evidence or bad.
Now, of course the Times Opinion section as a whole can provide daily models of "logical arguments based on substantive claims," whether through the Editorial page, Op-Ed columnists, Letters to the Editor or even the collection of Opinion videos.
Dr. Phil A man's wife lashes out at him daily, leading to violent arguments in front of their young daughter.
