see below the reasons turkey is kosher, if they are correct it seems that
a bird that did not have a mesora can get one
only if jews are eating it according to: Meishiv Davar, Tzemach Tzedek,
just by testing it according to: Arugas Habosem, Shoel U’Meishiv
but according to Rabbi Hershel Schachter, Kaf Hachaim, it can not get a mesora at all
Meishiv Davar, YD 22 (R. Naftali Tzvi Yehuda Berlin) says that when the turkey (indik) was brought from India there were questions regarding its kosher status, and therefore some people refrained from eating it. However, since the majority of people accepted it as kosher, unless there is evidence that it is not kosher, we are not going to say that it is prohibited post facto (especially not to tell people who were eating it for many years that they were doing so in error). Also, perhaps Ramah only requires a mesorah on a bird that was not eaten by Jews in the past. However, a bird that was eaten for many years and has all three simanim of a kosher bird is permitted even according to Ramah. There is no reason to say that all the people who ate turkey did so in error.
Arugas Habosem (pp. 16) says that the mesorah is only required to prove that it is not a doreis. If the bird is monitored for at least twelve months, one may rely on the kosher status of the bird even without having a mesorah on it, as it is obviously not a doreis.
Kaf Hachaim (82:21) says that the mesorah originated from the Jews in India and is thus permitted. Similarly, Rabbi Moshe Heinemann (Star-K, Baltimore) feels that since it’s called oaf hodu, it came from Hodu (India), and the Jews there had a mesorah on it.
Tzemach Tzedek (YD 60) says the fact that a specific bird is eaten is a form of mesorah.
Shoel U’Meishiv (5:1:69) posits that turkey has all three simanim and is not a doreis, end of story. And what of the Ramah about needing a mesorah? There is no mesorah for a turkey, and it must be that klal yisrael did not fully accept this Ramah. In other words, we do not hold like Ramah’s opinion, and if a bird has the simanim which indicate a kosher status we may eat it even without a mesorah.
Rabbi Hershel Schachter: Columbus was from Spain, and so when he returned from America back to Spain, he brought the turkeys back with him. Thus, the mesorah we have today comes from the Jews of Spain, who have a long and rich history. Or, Columbus discovered America 1492, some 48 years before Ramah was born (in 1540). Thus, it seems that a sound sevara would be that Jews began eating turkey based on its kosher simanim alone, without a requirement for mesorah, as Ramah didn’t write his opinion yet!
But it seems that songbirds might have a messora,
There are other birds such as partridges and songbirds which have been consumed for thousands of years, their consumption originating in a time when people still recognized the forbidden birds listed in the bible
PS Rabbi Chaim Loike from OU researches this subject
PPS maybe there source of Rabbi Heinamann's opinion is from this video Chickenar (11/12/2012) by 9:38