Generating SMPTE time code signal
This is not a task for the inexperienced.
 You can buy SMPTE generators and if you need one and can afford a commercial one that would be the easiest path.

Next easiest, if PLCC44 and TQFP44 are easy, is probably the ICS2008B from Intergrated Circuit Systems Inc.
 ICS2008B SMPTE Time Code Receiver/Generator datasheet 

The task itself doesn't look too too difficult. Actual code is "like NRZ but different" (SMPTE = A transition at every bit boundary plus 1 = a transition at bit centre). That's the easy part. You could probably "roll your own" with many microontrollers, but the timing synchronisation is probably the 2nd hardest part and understanding the specification may be hardest. Even using an ICS2008BV would be"interesting".

Wikipedia gives a fair idea of why you don't want to roll your own. Their explanation of drop frame time codes where no frames are dropped but frames 0 and 1 have time code dropped in the first second of every minute except when minutes are divisible by 10, all this to remedy a multiplication by 1.001 that was introduced due to colour NTSC because  ... , reminds me of an extremely old poem about Inuits making fur moccasins. "The skin side is the inside but the inside's on the outside and the fur side ...". At least the poem was trying to be confusing*.

Do it with a Mac - SMPTE TO Midi donationware

Useful intro discussion - if you can't follow this, buy a commercial unit.
 If you can, buy one anyway :-).

SMPTE / MIDI slideshow. Some value



* A little Gargoyling shows it was, in fact,   


"The Song of Milkanwatha"