Tahanun (supplication prayer) is not recited the entire month of Nissan. The reason for this is that since the majority of the month is holy we consider that the entire month is holy. The breakdown of the days is as follows:
On the first of Nissan the Mishkan (Tabernacle) was erected. and each of the Nesiim (Princes of the Twelve Tribes) brought their offerings. Each Nasi (Prince) brought his offering on one day. This lasted, therefore, for twelve days, and each day was a Yom Tob (holy day) for the one who brought that day's offering.
The following day (the thirteenth day) was their Isru Hagh (the day after a holiday which also contains holiness). The day after that is 'Ereb Pesah (the eve of Passover) which is also holy. After that we have 8 days of Pesah (Passover), plus the Isru Hagh which, as we mentioned, also has holiness attached to it. And since the majority of the month passed in holiness, we consider the entire month to be holy.
There is an opinion, however, that the remaining days of Nissan also have their own Qedusha (holiness) and we will look at that, (beli neder), tomorrow.
(See Shulhan 'Aruch 429:2 and Rama. Kaf Hahaiim ibid, 21. Mishna Berura ibid, 7.)