So I'm not aware of any serious "successful" (by whatever metric they had for themselves) initiatives in this regard, especially not such highly specific ones, I will note that this was a general goal for a lot of American eugenicists. They wanted white, and especially "Nordic" (the highest classification according to scientific racism), families to have at least four children in order to perpetuate the race against race suicide, and in whatever public roles they had often urged WASP couples to do so.

However much eugenicists may have believed in their cause, though, it doesn't seem like it was quite enough to spur them to actually help out in the effort- many of the leading eugenicists were childless.

Now, on a more general level this is something that was observed not just about eugenicist thought leaders but about the very kinds of WASPs who the eugenicists particularly wanted to encourage to procreate to prevent race suicide in the wake of Irish, Italian, Jewish, and Eastern European immigration, not to mention the proliferation of people of color. Theodore Roosevelt was a believer in procreation as a way to prevent race suicide, believing that the average WASP family had to have four children to allow them to outpace the rapid growth of minority and immigrant communities, but bemoaned that upper-class families were being selfish and committing “the capital sin, the cardinal sin, against the race and against civilization.” To TR (who put his money where his mouth was and had six children), it seemed clear that upper-class white families were putting their own comfort and lifestyle as priorities in choosing not to have more than one or two children, if that many. As he once told a friend, “They seem unable to see that it’s simply a question of the multiplication table. If all our nice friends in Beacon Street, and Newport, and Fifth Avenue, and Philadelphia, have one child, or no child at all, while all the Finnegans, Hooligans, Antonios, Mandelbaums and Rabinskis have eight, or nine, or ten—it’s simply a question of the multiplication table. How are you going to get away from it?”

As much as these realizations may have frustrated those who were involved in eugenics and scientific racism, especially as they were often matched by a lack of interest among the "lesser races" in the birth control options which were the other prong in their effort, at the end of the day the eugenicists were extremely prominent examples of their own (self-declared) problem. Many of the most famous and influential eugenicists, like Madison Grant, Houston Stewart Chamberlain, John Harvey Kellogg, Kenneth Roberts, Harry H Laughlin, and many others, never had children (and even those who did didn't necessarily focus on replacement rates- Lothrop Stoddard, who I discussed here, was one of the leading figures who did produce children but had only two). The leader of the American Eugenics Society noted despairingly that 10% of the members of the advisory board were unmarried and 25% were childless. And, of course, if one looks at the eugenics movement writ large, its originator Sir Francis Galton and the man who took it to its horrifying conclusion (Adolf Hitler) were both childless as well.

When noting this, some scholars note, in the same breath, how these men seemed so riveted by and emphatic about castration, sterilization, and prevention of race mixing. The childless were some of the biggest proponents of these efforts in a practical sense, which often leads scholars to draw lines from the puritanical notions of sex with which many of the eugenicists were imbued and their attitudes toward eugenics- including pointing out how often the term "cut off" is used in eugenicists' descriptions of eugenic practices. Similarly, some of the same eugenicists and racists who focused their efforts on preventing miscegenation used sexually charged language to do so (talking about the desire of mixed-race men to "thrust themselves" into the white race, for example) also spoke loudly against the evils of female masturbation. Puritanical attitudes seem to have been quite common among many of these men and to have potentially come from the same well (or rather contributed to) their interest in eugenics.

Ironically, it may be that this lack of reproduction was a large part of what led to one particular group dying out- the eugenicists. While of course there is nothing hereditary about being a eugenicist, by the 1930s, as the group's childless leaders were growing old, their societies fell apart and became less and less effective (soon after having reached their peak in the early-mid 20s with their role in creating US immigration and racial policy). There was basically nobody there to replace them in dad's old hobby- even before the Nazis began to invoke eugenic policies themselves, to worldwide disgust.