Baku Regenerates, but the first barn upgrade is required to take them home
Beaklon Have your monster look around the western side of the ranch sometime in August, from year 1004 onwards; you will find a yellow crystal which triggers an event in which a Beaklon visits your ranch. Beaklon can then be regenerated at the shrine, but cannot be taken to the ranch until you get the first barn upgrade
Colorpandora Available from the start
Dragon Get a monster to Rank B. Sometime in January, you will be invited to a Rank B Invitational on the 3rd of February, where you will fight a Dragon. Defeat the Dragon to get the Dragon Tusk. Dragon can then be regenerated at the shrine, but cannot be taken to the ranch until you get the second barn upgrade. The item can be used in combination to give you a Dragon-Modoki (Dragon/?) (NOTE: The Dragon is extremely strong for a B-Rank monster. Be prepared)
Ducken On the forest Venture, knock down and cross the first bridge; on the other side, search the southernmost area for a Quack Doll. Ducken can then be regenerated at the shrine. The item can be used in combination to give you a Ducken-Modoki (Ducken/?)
Durahan Find the Sheath and Sword on the arctic Venture; upon returning, the carpenter will notice the items and repair them to make the Double Edged. Durahan can then be regenerated at the shrine. The item can be used in combination to give you an Omoroknight (Durahan/Ducken)
Falco Available from the start
Golem Regenerates, but the first barn upgrade is required to take them home
Hare Available from the start
Henger On the pyramid Venture, search the area for five Henger parts (they are far apart, so multiple trips may be necessary); two in the bottom-left room, one in the left-most room at the northern intersection near the entrance, one in the top-right corner of the map and one in the right-most corridor on the way there. At the ranch, the scholar will come over and assemble a Henger Doll using the parts. Henger can then be regenerated at the shrine. The item can be sold for 3000G or used in combination to give you a Pulscorn (Hare/Tiger)
Joker On the island Venture, search the easternmost clearing to find a Joker Mask. Joker can then be regenerated at the shrine. The item can be sold or used in combination to give you a pure Phoenix
Lesione On the island Venture, head to the beach; you will see a Lesione swimming around near the shore. Lesione can then be regenerated at the shrine
Mew Compete in several tourneys to raise your monster's popularity; the mailman will deliver a Mew doll to you from a fan. Mew can then be regenerated at the shrine. The item can be used in combination to give you an Eared Mew (Mew/Hare)
Mocchi Available from the start
Ogyo On the forest Venture, knock down and cross the second bridge. You will find a Goldfish Bowl on the other side. Ogyo can then be regenerated at the shrine. The item can be used in combination to give you an Ogyo-Modoki (Ogyo/?)
Phoenix On the jungle Venture, go to the top-left area of the map and knock down one of the trees blocking your path. Search the other side to find a Phoenix Feather. Phoenix can then be regenerated at the shrine. The item can be sold or used in combination to give you an Ambush (Henger/?)
Piroro Available from the start
Pixie Available from the start
Plant Available from the start
Suezo Available from the start
Tiger Available from the start
Xenon On the pyramid Venture, search the bottom-right room for a mysterious white shard. Afterwards, search the left-most room at the northern intersection near the entrance for a mysterious red shard. At the ranch, a scholar will come over to inspect them. After some elaboration, he will take them. Afterwards, return to the pyramid and search the room where you found the mysterious white shard for the King's Crest. At the ranch, the scholar will return to inspect the crest, explaining its connection with the Xenon monster. Xenon can then be regenerated at the shrine, but cannot be taken to the ranch until you get the first barn upgrade. The item can be sold or used in combination to give you a Zanzo (Suezo/Zan)
Zan On the jungle Venture, go to the bottom-right corner of the map and knock down one of the trees blocking your path; after searching the area, a wild Zan will appear. As it walks away, it will drop a Ninja Sword. Zan can then be regenerated at the shrine. The item can be used in combination to give you a Shibasa (Zan/Falco)