As of the "4 more years" update, only one challenge mode is available (Born again). I had some ideas for some other challenge modes. Here they are:
Grandma's wrath: The Grandmapocalypse at its last stage starts when you get to 1 billion cookies, along with all the upgrades from the Bingo Center being purchased immediately. However, Elder Frenzies are twice as likely to happen, which can be used for getting more Prestige/Heavenly Chips faster.
Ultragold: CpS production is halved throughout the ascension, but all the Golden Cookie upgrades (Lucky day, Serendipity, Get lucky) are auto-bought, and Golden Cookies appear twice as often and last twice as long AND have their effects last twice as long even with all the upgrades being auto-bought. It would be possible to have an Elder Click Frenzy Frenzy or something ridiculous like that.
Insane mode: Everything costs twice as much. However, it produces twice the heavenly chips and prestige as a normal ascension. Would only be for the bravest.
Those are my ideas. Comment more below if you want.