I don't know about SRAdb or what metadata that database contains, but you can use entrez to search SRA with the normal limits (including organism)

library(rentrez)

entrez_search(db="sra", term="Tetrahymena[ORGN]")
# Entrez search result with 113 hits (object contains 20 IDs and no cookie)

It looks like tissue isn't a specified term for tissue

> entrez_db_searchable("sra")

Searchable fields for database 'sra'
  ALL      All terms from all searchable fields 
  UID      Unique number assigned to publication 
  FILT      Limits the records 
  ACCN      Accession number of sequence 
  TITL      Words in definition line 
  PROP      Classification by source qualifiers and molecule type 
  WORD      Free text associated with record 
  ORGN      Scientific and common names of organism, and all higher levels of taxonomy 
  AUTH      Author(s) of publication 
  PDAT      Date sequence added to GenBank 
  MDAT      Date of last update 
  GPRJ      BioProject 
  BSPL      BioSample

But you could search for biosamples that match you query, then find links to SRA?

entrez_search(db="biosample", term="Mouse[ORGN] AND Tissue Liver[Attribute]")
Entrez search result with 2934 hits (object contains 20 IDs and no cookie)

Could SHARQ be something like what you're looking for?