Why can't I use "easierly" instead of "in an easier manner" or "more easily"?

Historically, people interested in expressing the idea "more easily" in a single word seem to have preferred easilier to easierly. Here are the Ngram results for easilier (blue line) versus easierly (red line) for the period 1750–2000:

The results are actually skewed in easierly's favor by multiple OCR misreadings of easterly as easierly; such misreadings account for the great majority of the early reported matches for easierly. In contrast, most of the matches for easilier are legitimate; and the frequency of its usage increases the farther back in history you go. Here is the corresponding Ngram chart for 1600–2008:

Nevertheless, instances of easierly do exist, perhaps most prominently in this sentence from Fenimore Cooper's The Deerslayer (1841):

"Hark'ee, Sarpent," he [Deerslayer] continued more gravely, though too simply for affectation ; "this is easierly explained than an Indian brain may fancy. The sun, while he seems to keep travelling in the heavens, never budges, but it is the 'arth that turns round ; and any one can understand, if he is placed on the side of a mill-wheel, for instance, when it's in motion, that he must sometimes see the heavens, while he is at other times under water. There's no great secret in that, but plain natur' ; the difficulty being in setting the 'arth in motion."

A more recent instance occurs in ISEC '88: International Solvent Extraction Conference (1988):

In standard cases more effective extractants will demonstrate higher selectivity since they easierly enter the inner lantanide sphere destroying the hydratic sphere and forming corresponding solvates or complexes (for example, helato-forming reagents.) (Fig.7-9).

So, yes, you can say "easierly" (or "easilier") instead of "in an easier manner" or "more easily"—and after a moment's thought, most of your listeners or readers will probably understand that you are using the word to mean "in an easier manner" or "more easily." They may also think, "Why is he using that weird word instead of the phrase that everybody else uses?" But such is the price (as Fenimore Cooper well knew) of rejecting the familiar paths of common language and striking out across the untrammeled wastes of possible language, a pathfinder in one's own mind.