How many rent tokens can I put in my lockbox for rent?

There is no fixed limit per se, but like coin, you can have up to 8 weeks rent in your lockbox at once.

If you are going to be away for an extended period, it would be wise to fill your lockbox. Lockboxes will hold enough gold to pay for up to 8 weeks of rent. This will help ensure that you have enough coin when the rent is due so that your house is not repossessed while you are away.