Same thing happens with the word "cnoc" = hill, which is pronounced by most natives as "croc".
It's certainly not in Munster Irish.
Traditionally the preposition ar is used with the noun cósta. This can be seen in Ó Dónaill's entry for cósta as well as the numerous results in the Historical Irish Corpus for ar chósta and ar an gcósta. No results are returned for either ag cósta or ag an gcósta. Sean Caomhánach, in his Irish only dictionary, describes gaineamh as le fagháil ar an gcósta nó ....
In light of that the sentence here should probably be amended to Snámhann na mná ar an gcósta