Okay, bouncing off some of the heir ideas suggested above, what if the condition is that the BBEG has to take a Succubus as his wife?

The intent would be for the succubus to birth literal devil-children, who would nevertheless be the rightful heirs and able to use the power, influence, authority and trust of the monarchy to corrupt a great many souls in the kingdom.

The devils would be happy to protect the king, as he would be necessary for this plan to succeed. Though, after he'd fathered a few children, he might have outlived his usefulness. ;)

As far as summoning the devils, could the BBEG have done so in a secluded place, far from the palace (probably not the sort of thing you'd want a servant walking in on!)? Perhaps even some unholy shrine he'd stumbled across (or been led to)?

Given that many devils can teleport and/or change form, the demons could have remained with him afterwards, disguised as dogs, servants or the like. Others could make themselves invisible and quietly remain within teleportation distance, ready to jump to his side should the BBEG summon them.

If the BBEG needs to summon more demons he could, as you say, send a trusted minion or such to do so.