For Palaearctic have a look at "A. S. Konstantinov · B. A. Korotyaev · M. G. Volkovitsh. 2009. Insect Biodiversity in the Palearctic Region (chapter). There are numbers of described species in Coleopteran families based on Catalogue of Palaearctic Coleoptera. You can download it from my page in RG. Also "Parker, S. P. (ed.). 1982. Synopsis and classification of living organisms. Volume 2. McGraw-Hill Book Company, 1232 pp.", but I'm afraid it's too old. Certainly, you can find some data in Internet.

Good luck,

Mark

Coleoptera currently includes 176 families, 29500 genera and 386500 species, fossil taxa includes 31 families, 230 genera and 600 species. Copy from  Slipinski S. A., R. A. B. Leschen, and J. F. Lawrence. 2011.  http://www.mapress.com/zootaxa/2011/f/zt03148p208.pdf

The two volume set of American Beetles gives estimates (world-wide) for most of the families covered.

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