I have been able to install tiny core on second partition(ext2) of my USB stick(16GB , first being fat 32 to be read on windows and linux OS).
Here is what I did
mounted coreplus.iso to /tinycorecd
gave /tinycorecd/boot folder for core.gz
selected frugal , existing partition , install boot loader , mark partition active bootable
waitusb=9 option
core and x desktop - nothing else selected
When I boot from USB , I get a 'tiny core' entry which on entering drops me to a prompt with $. no X window.