Artists illustrating early works on fossils were at a disadvantage. If they wanted to show the actual creature, they had no model. If they wanted to picture the fossils, they often still had no model. So artists turned to earlier illustrations.
Trying to identify the originals of illustrations is like trying to zero in on in just what millisecond the Big Bang occurred. Illustrators copied from illustrators who copied from other illustrators. However, Martin J. S. Rudwick's readable and lushly illustrated Scenes From Deep Time: Early Pictorial Representations of the Prehistoric World (Chicago: University of Chicago Press, 1992) helps to set the illustrations in early American works for children in context. Many of the illustrations appear to have been copied from Gideon Mantell's The Wonders of Geology, which was published in London in 1838 and in the United States in 1839. Others may have originated in Peter Parley's Wonders of Earth Sea and Sky, published in London by Darton & Hodge in 1837.
In identifying the sources of a number of the illustrations, I've relied heavily on Rudwick's book. Unfortunately, I've not seen a copy of the Darton book; the Mantell is available online at google books, but each volume seems to be from a separate edition. So these identifications are preliminary and a bit cursory.
A list of the illustrations in the transcribed pieces organized by subject appears at the end of this page.
in the American edition of The Wonders of Geology, by Gideon Mantell (1839); it very much resembles one by Rudolf Hofmann and Ludwig Becker which had appeared in 1836:
[image from Rudwick, p. 70]
in Wonders of Geology, by Samuel Goodrich (1845)
in "Letters About Geology," by "Professor Pickaxe" (1853)
in the British edition of The Wonders of Geology, by Gideon Mantell (1839)
from Wonders of Geology, by Samuel Goodrich (1845)
in the British edition of The Wonders of Geology, by Gideon Mantell (1839)
from Wonders of Geology, by Samuel Goodrich (1845)
in Geology and Mineralogy, by William Buckland (1836); two pterosaurs cling to a cliff face while another flies in from the back [image from Rudwick, p. 69]
"Letters About Geology," by "Professor Pickaxe" (1853); the clinging pterosaur appears to have been copied from the one on the right in the original
from Peter Parley's Wonders of Earth, Sea, and Sky [image from Rudwick, p. 75]
from Wonders of Geology, by Samuel Goodrich (1845)
"The Country of the Iguanodon," by John Martin, in Gideon Mantell, The Wonders of Geology. Preying on one reptile, the mighty (pudgy) iguanodon is attacked by another, as an excited pterodactyl looks on; the Cretaceous is a violent place. [image from Rudwick, p. 79]
"The Iguanodon," by Hammatt Billings, in Robert Merry's Museum (1842). Alone, the mighty iguanodon (much slimmer) roars to the sky; the little pterodactyl has been moved from earth to sky, though the wings are pretty much in the same position.
in the American edition of The Wonders of Geology, by Gideon Mantell (1839); it is based on outlines of two Palaeotherium and two Anoplotherium by Charles Laurillard, from Georges Cuvier, Researches on Fossil Bones, 2nd ed. (1822):
[image from Rudwick, p. 37]
from Wonders of Geology, by Samuel Goodrich (1845) The images are reversed, as if the artist copied the Mantell illustration directly onto the block and engraved it; the image prints in reverse.
unnumbered, unlabelled, and unnamed, in "Wonders of Geology," by William Buckland, in Robert Merry's Museum (1848)