I have just started playing soul silver and noticed that many mystery gifts have already come and gone.
Some Mystery Gifts in Generations IV and V are still available through the DNS Exploit, a process that takes advantage of the games' DNS settings to access old events. Any event accessed through this method is legitimate and will pass hack checks. Not every old event is available; for a complete list, and a guide on setting up the exploit, please reference the links below.
How to obtain all the Gen 4/5 mystery gifts? (Pokemon Database) How to unlock Gen 4 and 5 Pokemon Mystery Events in 2018 (Shacknews)
For other generations, your best bet is to trade with someone that received the gift. There are no similar exploits.
The only ways are trading for them on serebii or AR which is cheating.