Technically, as per Merriam-Webster:
: being before noon —abbreviation AM, a.m., or (British) am
: being after noon —abbreviation PM, p.m., or (British) pm
Strangely, neither Merriam-Webster nor Oxford let me look up just meridiem (they redirect me to either ante meridiem or post meridiem, respectively).
The Online Entymology Dictionary does, however, have an entry for meridiem:
mid-14c., "noon," from Old French meridien "of the noon time, midday; the Meridian; southerner" (12c.), and directly from Latin meridianus "of midday, of noon, southerly, to the south," from meridies "noon, south," from meridie "at noon," altered by dissimilation from pre-Latin medi die, locative of medius "mid-" (from PIE root *medhyo- "middle") + dies "day" (from PIE root *dyeu- "to shine"). Cartographic sense first recorded late 14c. Figurative uses tend to suggest "point of highest development or fullest power."
So, one of the following might be correct:
. . . change the meridiem designator.
. . . change the noon designator.
However, even if one of those phrases is correct, it's doubtful that it would actually be understood. Further, your instructions are not accurate in every case anyway.
For instance, if it's 10:30 a.m. in India, then it's actually 1:00 a.m. (not p.m.) in New York. Additionally, even if you do change from a.m. to p.m., you also need to change the date to the previous day. All of which seems more confusing than it's worth.
As was mentioned in a comment, it's more accurate (and probably more understandable) to simply say:
New York is nine and a half hours behind India.