[Phanx]

This should probably work:

local ringSpells = { [187611] = true, [187614] = true, [187615] = true }

local f = CreateFrame("Frame")
f:RegisterEvent("COMBAT_LOG_EVENT_UNFILTERED")
f:SetScript("OnEvent", function(f, event, _, combatEvent, _, sourceGUID, sourceName, sourceFlags, _, _, _, _, _, spellID, spellName)
	if combatEvent == "SPELL_CAST_SUCCESS" and ringSpells[spellID] and bit.band(sourceFlags, COMBATLOG_OBJECT_AFFILIATION_RAID) > 0 then
		local message = sourceName .. " used a legendary ring!"

		-- Post to own chat frame:
		DEFAULT_CHAT_FRAME:AddMessage(message)

		-- Post to own raid warning frame:
		RaidNotice_AddMessage(RaidWarningFrame, message, ChatTypeInfo["SYSTEM"])

		-- Send to instance/raid/party chat:
		-- SendChatMessage(message, IsInGroup(LE_PARTY_CATEGORY_INSTANCE) and "INSTANCE_CHAT" or IsInRaid() and "RAID" or IsInGroup() and "PARTY")
	end
end)

Comment or uncomment the lines for different message outputs as desired.