Thank you very mcuh for your query to Ireland Reaching Out. Do you know when the emigrated from Ireland? If you know the name of the ship, then you should check for more detailed information at the port of arrival in the US. This information was generally gievn at the port of arrival rather than the place of departure.
Do you have any idea about what part of Ireland they came from? This is important, as then you can start to check records and narrow it down somewhat. If they died in the US, try checking local newspapers for death notices. This could provide you with a little more information too. Check the cemetery in Burlington, as they may have registers which you could check.
Do you have any other relatives you could speak to? They may have other family documents which will help you get started in your research.
Once you know what part of Ireland they came from, you can then start checking census records, church records, etc.
Best of luck in your research!