http://revach.net/article.php?id=4152

Section: Tefila   Category: Tefila
Mizmor LiSoida: Rav Shlomo Zalman Auerbach & Rav Chaim Kanievsky ybcl"c - Is It Really A Song?
The Shulchan Aruch (OC 51:9) says that Mizmor LiSoida should be said "B'Negina", which literally means with a tune.  Rav Chaim Kanievsky says that this means it should be said slowly and sweetly.  Rav Shlomo Zalman Auerbach understood this very literally and even asked why we don't sing it in Shul just like we sing Keil Adon on Shabbos.

Rav Alexander Mandelbaum in his Sefer Aromimcha suggests that the reason we are not Noheg to sing it is because many people are not noheg to say Pisukei DZimra together with the Tzibbur.  If so, since each person will say Mizmor L'Soida at a different time, it will disturb the people around him.  Since to sing it is only L'Chatchila, it is better to say it, and not sing it and disturb other Mispalelim. 

The lesson that we can learn from here, says Rav Mandelbaum, is that no matter whether you sing it or not, Mizmor LSoida should be said slowly and with Kavana and HaKoras HaTov to Hashem for all the good which he has bestowed and continues to bestow upon us.