Using SD card to replace data cassette

After looking at the signal for a few more minutes, it seems clear that the clock signal is about 4166 Hz and the data are Manchester encoded.

Arbitrarily assigning a L->H transition as a "1", a very long sequence of 1/0 preamble is followed by a 11 start and then the data, so the first few bits including the "11" sequence are as shown below. Of course the inverse assumption leads to a "00" start followed by inverted data bits.

The lower track is a 4166 Hz square wave generated by Audacity, aligned so that the bits may be read off directly from the signal transitions occurring on the falling edge of the clock.

There is an Arduino Manchester library at GitHub - mchr3k/arduino-libs-manchester but it is pretty specific for transmitting and receiving short messages by radio and does not appear to be very well written. If you want to decode the data, I would suggest to start with one of the two decoding options presented by Atmel at http://www.atmel.com/images/atmel-9164-manchester-coding-basics_application-note.pdf