The Jack and Jill Foundation is calling for the new National Children's Hospital to be moved from its proposed site at St James' Hospital.
The head of the children's charity, Jonathan Irwin, says hundreds of families have told him they are opposed to the Dublin 8 location.
Last week the Department of Health said a design team for the new hospital would be in place by the end of the month.
The Minister for Health, James Reilly, has rejected the call, saying the Dublin 8 site is the best choice "by a country mile".