If beauty is not a property, because it is subjective, then why is the color red a property? Seeing a color is subjective, not only it is subjective, but we cannot confirm we see the same color, and some don't. What's the property that differentiates beauty to the color red as property? And if beauty is not a property is beauty based on a lesser property like coherence or harmony?
Frequency is a >>physical<< property; but, like you say, color isn't. It's more a qualia. Along those lines, and just like you say, "we cannot confirm we see the same color"
Quantitatively, consider the usual r,g,b colorspace, e.g., https://en.wikipedia.org/wiki/RGB_color_space But suppose you and I are born differently with respect to our r,g,b qualia -- my "red experience" is your "blue experience" (and, say, my green your red, and my blue your green). So, e.g., when we both look at the same apple, I'm having my red experience, whereas you're having my blue experience.
But we've both been taught to say the word "red" to describe our respective-but-different experiences. Moreover, for any combination, e.g., red+blue=purple, we'll have correspondingly different experiences, but have learned the same word. So it's logically impossible (i.e., by manipulations of symbolic information acquired by talking to us) to determine whether or not you and I are having the same color experiences (it might be physiologically possible, maybe by some kind of fmri-like brain scans).
So it's only (the frequency, etc of) the apple's reflected light that's a property, per se, of the (beautiful or not) apple, not its "color". Likewise, "beauty" is a personal experience, but in this case it is logically possible to distinguish whether or not we're having the same "beauty experience" just by talking to us.
Problem of objective definition of beauty
For something to be a property, it must be objective, i.e. it must be independent from observer. From purely skeptical position, we could declare anything perceived empirically to be subjective. Yet, although strictly speaking true, this is not very practical - it reduces philosophy to infertile solipsism.
Therefore, let's use somewhat relaxed definition of property as something that could be objectively defined :) For the colors, usual definition would be frequency of light (electromagnetic radiation) visible to human eye. Although imperfect, this definition is at least mostly independent from observer. As such, it could qualify as property. But is there similar definition of beauty ?
In fact, although no definition of beauty is universally accepted , it is entirely possible to create such definition . One example would be functional definition of beauty - something is beautiful if it serves its purpose well. For example, primary function of sport car is speed. Therefore, sleek sport car is beautiful because aerodynamic improves speed. Tanks on the other hand must have good armor and firepower, therefore beautiful tank would be rugged looking and robust. With functional definition of beauty it is relatively easy to grade human made objects. Problem arises with things that do not have well-defined function. For example, what would be primary function of the women ? If we define it purely biologically as child bearing, we could reduce her beauty to attributes needed to have and raise healthy offspring. But of course such definition would be unacceptable to large parts of society.
From this, we could finally conclude : beauty could be considered as property if we could find generally acceptable definition of beauty. Since currently we could not do that, beauty is in the eye of beholder.