I contacted Bitt-Boy for a replacement cable. They didn't respond to my email.
Via Twitter they sent me a photo of the cable (which I already have), and told me to go on ebay and order a "Av line one minute two 2.5 RCA lotus line millet"
Which basically means take a risk and order a 2.5 mm AV cable from ebay.
Which Cable?
I had already bought a "nokia 2.5mm to RCA AV Audio Video out TV cable" but since (I assume) that has 3 connectors it didn't work. Shame. It was a super quality cable.
You might already have a cable
I tried the cable from another handheld TV Game a "Retro Games Controller" from Thumbs Up with "200 built in games". I hunted through all my direct to TV games and tried this one.
http://www.thumbsupuk.com/Products/Retro_TV_Games
And the cable worked fine - better than Bitt-Boy cable and probably 'good enough'. So cables from other devices might work. But it still screams 'cheap cable' and probably won't last if it is used a lot.
The Perfect Cable
I then took a punt on a "Fuji Finepix 2.5 mm AV Cable" which is really good quality and works well, provided you put the colours in the right way round. Using the bitt-boy white for video, yellow for audio.
I bought mine from ebay for the princely sum of £2.99 + 99p postage.