Before talking to an agent, you need to do some preparation. This can be from having the reference number on your application and also preparing on what to say to the agent. It also helps being a nice human being to this people when you talk to them. Do some small talk and ask how they’re doing, etc. : )

Here’s a script to use when you talk to an agent:
“Hello, I recently applied for (insert name of card) and was surprised to see that my application (was rejected/wasn’t instantly approved). I was hoping I could talk to someone to better understand this decision and possibly get it reconsidered.”

The Credit Card Accountability Responsibility and Disclosures Act (CARD Act) of 2009 requires issuers to explain to you in writing the reason your application was rejected. It’s very important to have this piece of information before you call the reconsideration line so you can politely explain to the agent why the concerns the bank raised aren’t relevant and you would, in fact, make a great customer.

Remember: the point of this call is to counter the reasons for denial. 

Lastly, this is very important, don't tell them specifically that your opening that card just for the sign up bonus. Instead, tell them that you like the benefits of that specific card (maybe mention one perk/travel benefits like bag insurance, etc.). Then, just listen to the agent and take notes on the reasons for the card denial.

Another potential way to get your application reconsidered is by asking them to move some credit lines from a current card and moving some of those “credit lines” to the new card you’re trying to get. For example, you have a current business card that has a line of credit of $10K - you can politely ask the agent to move some of credit line to that new card. Sometimes, it takes only moving a line of credit $3K from a current card to the new card and get approved! This worked for me a few times so I highly recommend mentioning this to an agent.