The following tip is only useful wenn you have plenty of monay and construction materials – else you will be poor very soon.
The bottleneck with nation reputation is the availability of missions to increase your reputation. To increase your chance for these mission, you need to have a settlement in 5-6 towns of a nation and a building licence.
The governor often offers mission to build a production building when the produced goods might sell well. You can make use of it.
You accept the offer, erect the building and your nation reputation will increase. Afterwards you can demolish the building – without any loss in nation reputation.
As long as the AI does not erect any building, the governor will offer you a new mission to build the next production building within 2-3 weeks.
If you proceed in this manner in 5-6 towns, the amount of available missions will be high enough to increase your nation reputation.
With a little luck you can get additional missions from famines or epidemics in a town. Therefore you should not supply these towns with any food or hospitals.