Dear Marcie,
One of Edinburgh's poor houses was in the 'Greenbank' area of what is now greater Edinburgh. It was situated opposite what was 'The City [fever] Hospital'
The difficulty when searching records is that when a birth or death happened there, was the address is listed as '144 Comiston Road' [quite a salubrious part of Edinburgh then and now] because the Lodge house was situated at 144 Comiston Road about 300 yards south of what is South Morningside School. The actual Poor House as about 1 mile west of Comiston road at the end of a very long drive, so the gentile lady's of Edinburgh would not be offended by seeing the Poor. only found this out when trying to trace the death of a relative who I knew was of very limited meens and found that they died 144 Comiston Road an then doing more research. The buildings are all still there and are now part of an upmarket development called 'The Steils'.