You need to find a Nintendo access spot. It should work wherever there is a wifi spot for the public. I don't know if it works for them all, but I do know Burger Kings with wifi should work. Nintendo hasn't really been helpful with this, but that's to be expected I guess...the game is super old now in retail gaming standards.
Hi! The presents are special DLC (short for Downloadable Content) in the game. They are special presents that Nintendo announces and give to players. They are only given between certain time periods. The last ever DLC given was early last year. You cannot time travel back to get DLC, which is why they are rare and often get asked for a lot in shops.
Some special DLC's where given out via Nintendo Zone. Nintendo Zone is a particular place that gives them out. One Nintendo Zone was Macdonnald's. If Nintendo announces a DLC in Macdonnald's, you could go to Macdonnald's, open up ACNL, go to the Post Office, ask Pelly for a present and—boom! There you have it! Your DLC. Unfortunately, Nintendo have stopped giving out DLC, so you can't get anymore. Some DLC were announced in different countries, depending on the items.
So, to briefly explain, there is no DLC available any more, that's why Pelly says there's no more presents available.
Thanks, and I hope you understand!