One of the best sources of information on model boiler design is the Australian Miniature Boiler Safety Committee. (AMBSC) The four books (1) Copper (2) Steel (3) Sub-miniature and (4) Duplex Steel
http://www.smex.net.au/Store/Store_AALS-Codes.php
Model Boilers & Boilermaking by K. N. Harris has a wealth of good design information and construction methods. Topics covered include fuel and firing and accessories. (Copper boilers)
Model Locomotive Boilers by Martin Evans is also a good source of design information and methods. It covers welding equipment, workshop equipment, water, fuel and combustion, oil and gas firing, and testing. The testing is more than a simple hydro a full engineering test stand designed by J. Ewins is described with drawings of the boiler and test results. (Copper and steel boilers)
Safety of Copper Boilers by Kozo Hiraoka this nine page article was first in
Live Steam & O.R. (Vol. 40 No. 6 Nov-Dec 2006) and is included in
Building the New Shay. The design rules are presented in graph form for simplicity with the ASME formulas and code designation listed in the appendix. All graphs have a metric and an imperial version. The graphs are (1) Minimum thickness for a cylindrical shell under internal pressure (2) Maximum allowable pitch of symmetrically arranged staybolts (3) Maximum allowable diameter of a circle enclosing an unstayed surface area (4) Minimum staybolt diameter. This book like all of Kozos books is a treasure trove of useful information for the model engineer.
These are the four main sources of model boiler information in my stack. Several other model engineering books I own have boiler chapters but the information is not a complete design system. These include works by Greenly, LBSC, Tubal Cain, and Martin Evans.
Cheers Dan