There is no way to know for sure, since these evolving buildings have been around less than a year, but some of us are hoping (and wishing, and praying) that they will again be offered during the Easter event in the spring. We do not know if there will be a new evolving building that will take the same artifacts (forcing a choice unless you gain enough artifacts for both), a new one that will take different artifacts, or no evolving building at all.
Evolving artifacts have also popped up a few other places, such as the Fellowship Adventures, but they seem to be quite few and far between. It would be difficult to amass 9 of them for your Phoenix in that manner.
Luckily, you can keep that birdie in your inventory until the spring and see, and then disenchant it for some nice spell fragments if you find you don't want to place it.