I suggest you perform a search on GEO (Gene Expression Omnibus) or ArrayExpress. A quick search with 'adipose tissue' returned quite a few relevant results for the two databases. It is also possible to restrict your searches for human data only.
I am however unaware of any specialised human adipose tissue database.
Hope this helps.
I'd look at BioGPS as this is something we once did to prioritize genes for candidate genotyping. More importantly, I would use expression QTL data. There is an excellent set from Zhong Schadt 2010 Am J Hum Genet 86:581 conducted in human omental adipose, subcutaneous adipose and liver. This study should also have the outright expression data in ArrayExpress or GEO (NCBI).
I, too, am unaware of any database specializing in adipose gene expression.
Genevestigator currently offers the largest curated collection of tissue specific expression (over 350 tissue and cell type categories).
It contains various types of adipose tissues and you can verify your findings across multiple species like mouse or rat.