So handwriting is secure between a pair; then all you need is some sort of authentication. Why not use a very simple random number generator? Each member of a pair knows it, of course, and they occasionally set up fresh seeds. Each day is one iteration. To 'sign' a message, one simply writes down today's random number afterwards. (You said handwriting is secure, so you don't worry about someone tampering with the message and making an authentic number testify to a faked message.)

What RNG? Dunno. Blum Blum Shub has a hilarious name, but the multiplying is a bit painful. Depending on how much accuracy you want, you could make up your own simple recurrence (imagine a list of 5 integers, which shift each day, and the first is defined by the sum of the last two modulo 5). But it turns out geeks have already discussed PRNGs you can do with mental arithmetic:

• http://ask.metafilter.com/191135/Help-me-get-random-numbers-by-mental-arithmetic
• http://blog.yunwilliamyu.net/2011/08/14/mindhack-mental-math-pseudo-random-number-generators/
• http://stackoverflow.com/questions/3919597/is-there-a-pseudo-random-number-generator-simple-enough-to-do-in-your-head
• http://ask.metafilter.com/20334/Random-sequences-in-your-head

For the looks of them, at least one suggestion should work for you.