Can a Private Motion only be brought up in the Assembly if one of the two cards have been drawn (which isnt all that often) or can any one declare a private motion if they desire before the voting on the other agenda's have started?

According to the Rulebook on page 11, in The Special Phases section, under The Assembly , Step 3 states:

3 . Vote on Private Motions: If there are any “Private
Motion” Agendas in the “Current Agendas” area of the
board, they are voted on before any other Agendas .

Therefore, it would seem that "officially"there must be a Private Motion Agenda in order for there to be a Private Motion .

Also, Step 4 states:

4. Declare Agenda Order: The Chairman decides the
order in which the three current Agendas will be put to
vote. (There will be fewer than three current Agendas
remaining if one or more “Private Motion” agendas were
already voted on in this Assembly.) The Chairman reads
aloud all the Agendas, in the order in which they will be
voted on .

which would imply that any Private Motions are from Agenda cards, as there is a definite limit to the number of Agendas each phase.

However, if your group would like to allow additional Private Motions, have fun with it. I would be intereted to find out how it affects gameplay.

We have tried the following with much success. It has actually improved gameplay:

At the start of the game, each player receives a "Private Motion" token (I use a laminated business card that was printed with "Private Motion" on one side and one of six player colours on the other).

During any Assembly in which a Baron is present, clockwise from the Chairman, any player may play his "one and only" private motion as per the normal rules.

As usual, crowns may be traded for influencing the subject matter and wording of the private motion, but each player only gets their one shot at playing their own "private motion" card.

We did this because so much was devoted in the rules to explaining private motions, and then they only put 2 cards in a huge deck of agendas! The ability to place a private motion is so much fun, especially to cancel a painful charge, office or law that was imposed, or to simply let you back into the Assembly.

I would be interested to have you try this option and give back any feedback on what you thought of it.