The second discourse was the Hemavata Sutta
There's not a great deal of chronological information given, so it takes some detective work to find out when particular discourses were given.
The Vinaya Mahāvagga is of some help. After the Anattalakkhaṇa Sutta, the Buddha taught Yasa, then his parents, and his four close friends. After that he met and taught the group of thirty youths called Bhaddavāggiya. That was followed by the episode when the Fire Sermon (Ādittapariyāya Sutta)
was taught to the fire-worshipping Kassapa Brothers.
Next, the Buddha went to Rājagaha to teach King Bimbisāra, but it only says that he gave a graduated teaching on generosity, morality, and the way to heaven, the disadvantages of sensual pleasures, and the benefits of renunciation, followed by a teaching on the Four Noble Truths.
See "The Buddha and His Teachings," by Venerable Nārada Mahāthera for some attempt at organising the first twenty-five years of the Buddha's dispensation.