Technically, if it's a land line port and still connected to an exchange that hasn't gone completely VoIP (that's a thing where I am), it might actually be possible to build a charger module that plugs into that port.

Would it be worth it, though? ... No.

Low power is supplied over old land-lines for the purposes of making telephones ring and powering other handset bits and pieces, within reason of course. Using it for anything else is undoubtedly illegal as phone lines aren't rated for huge power draws.

(If you're interested, there are videos online where people have hooked up LED lamps etc.)

But, let's say that module existed and was legal. Your niece still wouldn't be happy with it.

To avoid burning out to the telephone line, any such device would have to be a r e a l l y s l o w trickle charge.

I wouldn't even think about it for emergency power outages. A battery backup is a better option.