。
She had sparkling black eyes.
Literal
She [topic-は] sparkling black eyes [object-を] was-doing.
~をしている is a special descriptive use, not the literal 'is doing X.' When the object is a body feature or visible trait, をしている means 'has, possesses (as a feature)' — 青い目をしている ('have blue eyes'), きれいな声をしている ('have a beautiful voice'), 丸い顔をしている ('have a round face'). It's the canonical way Japanese ascribes physical descriptions to a person. The relative clause 輝く ('that shines, sparkling') modifies the noun phrase 黒い目 directly, without any joining particle — Japanese's no-fuss approach to relative clauses.