On pg. 59 n. 47 (where I refer to the inscription as
CIL I2.626), and pg. 482 (where I refer to the inscription as ILLRP 122) I use the forms ACHAIA and TRIVMPHANS from this famous inscription of Mummius supposedly dating from 145 BCE or shortly thereafter as evidence for the first attested spelling of a Greek aspirate with a stop plus h. (A picture of the inscription can be seen at http://www.flickr.com/photos/dandiffendale/2343690597/) In fact, there is reason to think that the text we have is a copy, perhaps from as late as the the 1st century CE—the date suggested by Kruschwitz 2002:140. If this is correct, then obviously we don't know if the letters H are from the original or the result of conscious or unconscious modernization. If we set aside the Mummius inscription, then the earliest examples of the stop-plus-h spelling are from the end of the 2nd century BCE, e.g. CORINTHIORVM (CIL I2.585 l. 96, 111 BCE) and DELPHIVS (ILLRP 337, 106 BCE, a bilingual inscription from Delphi).
Kruschwitz, Peter. 2002. Carmina saturnia epigraphica. Stuttgart: Franz Steiner.