I've been looking into this and the answer is not presently unless you edit the game files. I guess I disabled the RenPy game console at some point in the past.
I'll give this some thought because the default console could very easily ruin saves if used recklessly. Some sort of dedicated cheat menu or sandbox mode would probably be far safer, but of course also more time-consuming to implement.
Yes, lovers are randomly generated with different hidden attitudes towards raising children. Continuing to woo and interact with those characters that want children will result in them putting forth different proposals.
Once you have at least one descendant, rather than risk hiding your money and probably losing it between cycles, it passes on to the children, which will go on to become either successful aristocrats making your life easier in the next cycle, or just plain ungrateful bums.
The next step should generally be to continue visiting other places from the "Territories" menu option, gathering a party of Renascents from them, and then retrieve and research the relic's pieces from those territories marked with the jigsaw puzzle icon as they show up.
Here's a simple guide I made some time ago that might also be of help along with the contextual in-game tips at the upper right.
