The manual details how to dis-assemble the camera and it appears that the battery is soldered onto the MS-461 board. (Sony part #A-1818-410-A - I can’t find an image of the board which would help but once you have accessed it the battery would be quite obvious)
I only found a few supplier listings when using the part number to search online for the battery. You may have better luck.
If you can't find one by using the "Sony part number" usually most batteries will have their type or model number stamped on the battery.
So if you can't find a suitable supplier it may be a case of having to access the battery first and seeing if there is a type number on it and then searching for that.
EDIT:
On a hunch I searched for 175681311 which is a number shown in the supplier linked above and came up with this so it looks like the number is about right to use for searching and there are a lot more suppliers shown when searching this way, rather than using the Sony part number
Your model is not listed in the Sears link above but the battery is used in a lot of Sony cameras it seems, so highly likely it is the one
From the service manual it looks as if it is clipped to the MS461 board, not soldered, and is not supplied with the board so must be available separately.
Hi. I have dismantled two cameras. The battery is definitely soldered to the board. As to supply I was not able to find any suppliers here in Australia. I suspect that is was a "one off" that was made specifically for this camera, but in the U.S.A you may have better luck. Even if I could obtain a battery from the "states" the shipping/postage is so high as to render the project nonviable..
Hey, I’ve run into that same issue on a couple of Sony Cyber-Shot models. The internal Li-Ion battery (or capacitor, depending on the model) that retains date/time settings can be a real pain — especially since Sony doesn’t clearly document its exact location across all models.
Since you’ve done repairs before and used sites like iFixit, you might feel comfortable diving in — but yeah, layout and battery placement can vary quite a bit. In some models, it’s hidden near the logic board or underneath the main battery slot, which makes disassembly tricky.
I’ve had luck sourcing obscure replacement components from https://precisionzone.com. They mainly handle industrial electronics, but I’ve seen small format Li-Ion cells, capacitors, and support parts in their catalog — plus they do diagnostics and component-level repair services, which could be useful if you don’t want to risk going in blind.
Might be worth reaching out with your model number to see if they can help with a part or at least guide you.
Good luck — hope you get your Cyber-Shot back in action!