I noticed that you can pay for a gold membership with DC. Is there any way to earn it within the game itself?
No, just 500 DBC for AllAccess users per month. Additional DBC has to be bought for money. AllAccess can not be bought for DBC anymore for years
When did they re allow you to pay for Any part of membership with Daybreak cash!!!?? that ended way way back. if you see a membership option on the shopping-basket from in game, its a re-direct to the web site where you will need to use some form electric money payment ie. a credit type card.
AFAIK you can't earn DC in-game (other than the 500/month for subscibers). The closest thing would be earning enough PP to buy Kronos.
Many players buy/sell on the broker for big profits and pay for their AllAccess membership with Kronos bought with the earned Plat.