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You need a way to generate a psuedo random sequence that's synchronized. You can then use that random stream as something that works like a stream cipher.
Getting synchronized sources of random numbers like that isn't trivial, but it can be done.
To spitball a notion: get something like a small microcontroller that can drive a small screen, no wireless capabilities needed. Putting an implementation of something like the hotp algorithm on it will let you get some random data with each button press. That data can basically be used like a one time pad where you press a button each time you need more data. People decrypting the data just need to start at the same point in the sequence.
There are so many issues with this that I haven't thought of, but it's the most reasonable approximation of a pen and paper algorithm that has modern security levels and can be done in a reasonable amount of time.
Basically, you're going to want to look into stream ciphers. Since those can be done without feeding the data into them, it's possible to have a more disconnected system.
It's worth noting that against a governmental adversary, you're far more likely to be revealed via poor application of a custom crypto system than by a targeted bypass of a commonplace one.
If you're under suspicion, a cop can grab the piece of paper you did your work on out of the trash if you forgot to burn it and no decryption is required. Being physically readable, the key material can be seized and it's lost. If they have a warrant they can put a camera in your house and just record your paper.
With a cellphone, the lowest level of scrutiny that can use a backdoor that we know of would be a sealed fisa court order. Anything less official would require more scrutiny, since the NSA isn't going to send a targeted payload to the phone of a generic malcontent/domestic subversive.
Widely used crypto systems address an extremely wide array of possible attacks, most of which aren't related to the cipher but instead to issues of key management and rotation. This can give you guarantees about message confidentiality being preserved backwards in time if the key is stolen,cand only new messages being readable, as an example. (Perfect forward secrecy)
What you're looking for can be made, but you need to strongly consider if it actually makes you more secure, or less. Probably less.