Step 1: Find the target word.
Counting forward from March, April is 1st, May 2nd, June 3rd, July 4th, August 5th, September 6th, so the word to encode is September.
Step 2: Measure each letter's distance from e.
For any letter at or after e, find how many places it sits after e in the alphabet. A letter is capital exactly when that distance is an even number (0, 2, 4, ...), since the rule marks e itself and then every alternate letter after it. Letters before e always stay lowercase.
Step 3: Apply this to each letter of September.
S sits 14 places after e, distance 14 is even, so S is capital. e is e itself, distance 0, even, so it is capital. p sits 11 places after e, an odd distance, so p stays lowercase. t sits 15 places after e, odd, so t stays lowercase. The second e is distance 0 again, capital. m sits 8 places after e, even, so m is capital. b comes before e in the alphabet, so it stays lowercase regardless of distance. The third e is distance 0, capital. r sits 13 places after e, odd, so r stays lowercase.
Step 4: Combine the letters.
Putting these together in order gives S, E, p, t, E, M, b, E, r, which spells SEptEMbEr.
\[ \boxed{\text{SEptEMbEr}} \]