The Special Birthday Gift Items for characters who appear only in the 2nd Generation cannot be purchased but as you should have your own Kitchen, Forge and Workbench, you will have the capability to make all of them once you have sufficient Skill Levels and have taken the appropriate lessons in School. You may notice that all items that are designated as Special Birthday Gift Items for 1st Generation characters, including all the Eligible Girls, are items that are sold by Yue! As your character will be unable to cook or use the Forge/Workbench until the 2nd Generation and many of the items are Cooked Dishes or Accessories, it is only through purchase from Yue that you will be able to give proper Birthday Gifts in the 1st Generation.
No other item, however much the character professes to like it, will result in an acknowledgement of the individual's birthday. Although characters will confide the items they like best and those they detest most at specific heart levels, there is one 'secret' item that will be recognised instantly as a birthday gift. Rune Factory 2 is a little different from other Harvest Moon games where birthday gifts are concerned. In Rune Factory 2, Requests that appear on the local Bulletin Board are the most vital aspect of social interactions, but speaking to every one on a Festival Day raises heart levels and giving a specific item as a Birthday Gift will do likewise to a lesser degree.
YES NOFestivals and by remembering every one's birthday.