Unfortunately, heirs are not random, or based on any actions of the player. All the heirs are historically based on the births of real sons (or those who sort of 'succeeded' their lines, such as Tokugawa for Imagawa and Toyotomi for Oda). Although their lifespans are random, nothing can be done to increase the number of them. Your lord could be off galavanting around Japan you'd still be having sons born (in fact, sons will be born even if their historical father is dead).

An unfortunate side effect of the heirs being historical is that you wind up with some clans having two or three heirs all roughly the same age, which doesn't promote longevity. It also means that one squandered heir could be the end of your line. In reality, a samurai in that position work on fixing that issue (or adopt, if need be).