Pictures and video footage of brother and sister Harry and Jessica, aged six and five, were made public as part of an appeal by the Leeds branch of fostering agency Caritas Care and the charity Adoption Matters.
They are among youngsters having to wait longer for a permanent home because it is more difficult to find adoptive families for siblings and children aged over four.
Caritas Care explained that it publicised their situation as part of a specialist service it offers to help youngsters in need of a home after other methods had been exhausted.
The agency has been trying to find Harry and Jessica a home in Yorkshire.
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Susan Swarbrick, Caritas Care's Children’s Services Director, said: "Harry and Jessica are being featured as part of the Bespoke Family Finding Service, a partnership service offered by Caritas Care and Adoption Matters, both independent adoption agencies who together, have over 150 years’ experience in adoption.
"The service offers local authorities across the UK a tailored recruitment option for children who may have waited longer to find their forever family through adoption.
"For many of the children referred to the service, this could be their best chance of a permanent loving family through adoption as all other methods of family finding have been exhausted.
"Although featuring children in the media is not widely practiced, evidence has proven that using a child's real image and film footage as part of our family finding has successfully attracted families who may not have considered the same child 'on paper'.
"This approach has resulted in the service finding families for over 90 per cent of the children we have featured since the service began in 2015.
"We can assure the public that children’s local authority have given full consent for the publicity."