The next easiest way to win a tourism victory is probably to find a city state with a unique improvement that provides tourism on flight and spam that. Alternatively, play a civ like Ethiopia or Persia that has a Unique Improvement like this.
You can also go for a Reliquaries approach. Kandy and Voidsingers can help with this a lot, though Voidsingers relics come pretty late. Mt. St Michel is the classic martyr spam enabler. Cristo Redentor is also a big deal in a religious tourism focus, and it also helps make Seaside Resorts stronger.
Faith is still very useful since national parks are still a solid source of tourism, just generally inferior to rock bands. This has good synergy with Earth Goddess and Eiffel Tower. Naturalists did become cheaper recently.
Other decent sources of tourism include great works (writing has been nerfed but is still decent and can be boosted via printing), careful wonder spamming (wonders all provide a little tourism based on their era, but don't build crappy wonders for the sake of it, it's hammer inefficient), walls.
In general for tourism, getting to Flight and then Computers is always important as this provides huge boosts to your tourism output. Hence, a decent science game is always needed. Additionally, if you're going down the national parks line, a good culture game will help to get to conservation asap. But culture by itself does nothing for a culture victory, it's important to get to key civics but it's purely defensive when it comes to tourism. And of course, the standard rules of making sure you have open borders and trade routes with every civ in the game are important (these provide +25% and +50% tourism respectively towards that civ). Democracy tends to be the best government form for tourism games, though sometimes it's best to just have the same government as the culture leader..
Don't forget that you only earn tourism towards civilizations you have met. Try and meet all the civs as soon as possible.