N.Y. Shirt- Buy a travel ticket to New York on your v4 or v4.5, use it when your Tamagotchi is an adult, then log on to Tamatown and visit the travel agency.
Car- Visit the main area of the shopping centre on the first day of the month.
Maple Leaf- Same as N.Y. Shirt, but get a ticket to Canada instead.
Sumo- Same as N.Y. Shirt and Maple Leaf, but get a ticket to Japan instead.
Sceptre- Donate 20 000p to the Gotchi King in three or more donations, then visit the king's palace.
Milk Jug- Visit the Convenience Store in Guruguru Town.
Smoothie- Same as Milk Jug.
Photo ID- Visit the main area of the office once your Tamagotchi has a job.
Gold Disk- Visit The Tama Beat on the 5th, 15th and 25th of each month if I remember correctly. If it's not there, try the 10th, 20th and 30th instead!
Wedding Dress- Visit Forever Tamagotchi on the 10th, 20th and 30th of each month if I remember correctly. If it's not there, try the 5th, 15th and 25th instead!
Sword- Donate 70 000p to the Gotchi King then visit the king's palace. I believe you need the Sceptre first.
Shield- Donate 200 000p to the Gotchi King then visit the king's palace. I believe you need the Sword and Sceptre first. Once you get this souvenir, you get a royal costume item for free! The royal costume gives you a password for the Nintendo DS game Tamagotchi Connexion Corner Shop 2!!
I hope this is all correct!
Note that for the travel tickets, you must do each one separately. For example, if you have two tickets, one to Canada and one to New York, you must use only one, then visit Tamatown and get the souvenir, then use the other one and visit Tamatown again, or you will only get the souvenir for the most recent trip.