Occurrences of natural theology in the Oxford English Dictionary:
NATURAL 
       1. Of law or justice: Based upon the innate moral feeling of 
       mankind; instinctively felt to be right and fair,
       though not prescribed by any enactment or formal compact. Esp. in 
       phr. natural law: in political and legal
       philosophy and theology, doctrines based on the theory that there 
       are certain unchanging laws which
       pertain to man's nature, which can be discovered by reason, and to 
       which man-made laws should conform;
       freq. contrasted with positive laws; also (with hyphen) attrib. 

Cosmology
...1867 J. H. Stirling Schwegler's Hist. Philos. (ed. 8) 205 
   Metaphysics..are subdivided [by Wolff] into  Ontology, Cosmology, 
   Psychology, Natural Theology. 

Discredite
...1887 Spectator 29 Oct. 1456 Natural theology, he says, has become a 
   discredited science.

Educt
...1865 Reader 22 July 86/3 Throw revelation overboard, and its educt, 
   natural theology..must bear it company.

Less
...1880 Goldw. Smith in Atlantic Monthly 213 The foundations of natural 
   theology, less the mere name of Deity.

Natural
c. natural theology, theology based upon reasoning from natural facts 
apart from revelation. Hence natural theologian.

...1677 Gale Crt. Gentiles iii. 102 The Philosophers,..assuming a new 
   Divinitie or Religion of their own inventing, called..Natural Theologie. 

...1802 Paley Nat. Theol. Concl., These points being assured to us by 
   Natural Theology, we may well  leave to Revelation the disclosure of 
   many particulars. 

...1840 Macaulay Ess., Ranke's Hist. (1851) I. 129 Enigmas which perplex 
   the natural theologian. 

...1877 E. R. Conder Bas. Faith i. 16 If natural theology be regarded 
   as based on natural religion [etc.].

Physico-theology
...1825 Coleridge Aids Refl. (1848) I. 333, I more than fear the 
   prevailing taste for books of natural theology, physico-theology, 
   demonstrations of God from Nature, evidences of Christianity, and the
   like. 

Prolegomen
...1869 Kingsley Let. to F. D. Maurice 16 Jan., They are meant..as 
   prolegomena to natural theology.

Sick
...1961 N. Smart in I. Ramsey Prospect for Metaphysics v. 80 Natural 
   theology is the Sick Man of Europe.