I used to have a nice mod that would allow me to bully the Blades into keeping Paarhurnax alive, but after I did a cleanout it was no longer available. Yes, there are other mods out there, but I wondered: Is there a way to keep the old dragon alive and appease the Blades? Turns out there is-and it's a trick I've used in a couple of Dark Brotherhood assassination quests. I'm not sure how important, if at all, the steps are that I'm going to list, but this set worked for me:
1. Meet Paarthurnax and go through everything in Alduin's Bane, make sure to talk to him about meditating on Words of Power
2. To get Odahviing's name, talk to the dragon after talking to the Jarl of Whiterun (keep in mind I had finished the Civil War on the Stormcloak side before this [please do not get into a debate over which is better on this thread please]).
3. Complete the Main Quest line and talk to Arngier and the Greybeards (still don't know if they get angry over this-haven't tested).
4. Go to Sky Haven Temple. Esbern and Delphine will be upstares and outside-the old man will be speaking about some dream. Talk to Delphine and she'll give the quest, then click ',,,' and she'll congratulae you.
5. After speaking with her, open the console by pressing ` and type the following line without the quotes: 'setstage MQPaarthurnax 50' (you don't need to capitalize),
6. Merely talk to Delphine again and click 'About Paarthurnax...' and tell her he's dead and you're done!
Keep in mind this is merely the way I went through and MY steps-feel free to experiment with this and let me know how it worked for you!