In Tiny Core 1.1rc and beyond, the time zone is set via the kernel argument tz=. You need to know how your time zone is related to UTC/GMT (+ how many hours). See the references below if you don't know yours.

The only catch is that tz= reads its argument with a dash/minus instead of a cross/plus. For example, Melbourne, Australia is EDT+11 (UTC+11, daylight savings). For tz=, this will read EDT-11. To pass that to the kernel with GRUB:

root (hd0,0) kernel /tiny/bzImage tz=EDT-11 initrd /tiny/tinycore.gz

If you are using an ISO (CD boot), use tz=. Read about that arg by pressing F3.

To find how your time zone is related to UTC/GMT, visit timeanddate.com or google “UTC (your nearest major city)”

Wikipedia on UTC Forum Post - Tiny Core 1.1rc1 announcement and changes Forum Post - Use dash, not cross in tz= Forum Thread - Setting Time Zone in 1.0