I believe you're thinking of Haiti, but those buttons don't have the phoenix issuant from a Ducal coronet.
Foley's history is lost in the mists of time but the (presumed later) partnership with Croker has a listing in the Dublin Street Directory of 1862 as "Foley and Croker, button manufacturer and trimming warehouse, Foley H & Croker J" at 24 College Green, Dublin. Glenn Thompson from the National Museum of Ireland puts their date of operation between 1858-1868 so "H Foley" (solo) at the Cork Hill address is likely earlier. They seem to have predominantly made civilian and livery buttons.
See the button for the Seymour family at the link below, but note that there are stylistic differences (not unusual for heraldic interpretations) and also that Seymour may not be the only possibility.
If you hear hooves, think "horse" not "zebra" as the saying goes.