1>If a language is accepted by a DPDA then this language should have an unambiguous grammar.
2>This does not mean that all languages that have an unambiguous grammar is accepted by a DPDA (for e.g ww^r).This language has an unambiguous grammar i.e S-->aSa | bSb | epsilon
3>If a grammar is inherently ambiguous then it is surely not accepted by a DPDA.
In your question the language of valid parenthesis has an unambiguous grammar i.e S-->(S)S | epsilon..Thus there can be a DPDA though we are not sure because of point 2.
Now we try to make a DPDA that can accept it, to be sure..we get is as...say Q1 is initial state and Q2 is final state..then the transitions will be..
( Q1,(,Z )---->( Q1,(Z )
( Q1,(,( )----->( Q1,(( )
( Q1,),( )------> (Q1 ,epsilon)
( Q1,epsilon,Z)-----> ( Q2,Z)
therefore, this language is accepted by a DPDA