Device including RTC EEPROM and battery?
You're probably thinking of the M41T00CAP in the Timekeeper© series from STMicroelectronics. That is/was an RTC with integrated battery, and was housed in a DIP-24 package. Digikey still has them, and ST still indicates them as active, but it may be nearing end of life: those big DIL packages are not much used anymore. They also cost a multiple of what you would pay for a separate RTC and battery.  

RTCs with integrated battery offer little advantages over others, especially now that packages are really small, so that you only have to count the size of the battery. I think that's the main reason why you won't see them much anymore.  

RTCs will have some RAM instead of EEPROM. RAM is cheaper (you don't need the charge pump to generate the programming voltage), and since the RTC needs permanent power you have non-volatile memory for free. And RAM doesn't have a limited number of erase/write cycles.

A battery like the BR1225 has a capacity of 48 mAh, which will power an average RTC for 10 years continuously.