Like in Germany, the Autumn is often the BEST time of year. September, October and November can have beautiful weather with fewer extremes in temps. Also, fewer tourists and lower rates for some things.

Spring is OK too but weather is more variable and some places can be WINDY.

Bike rental is very expensive (IMO) at about $150 to $200 per day for a decent Harley. So figure at least $2,100 usd for 14 days. Now add insurance and "fees".

MORE TIME is needed. Do a longer ride. Maria's route (above)
seems a very good one if your parents MUST go in Summer. (June to September)

Weather in Colorado, Montana and Wyoming is good in Summer, not too hot. But her loop is a very BIG one with many thousands of Kms to cover. 14 days not enough. unless they ride HARD and FAST!

But they have many choices of different routes with various highlights that are ALL worth seeing. Most Germans I've met in the USA seem to really like Death Valley ... in Summer ... when it can be 48C !

Germans also like Las Vegas . (also hot in Summer) If they want to see Death Valley, Grand Canyon and Vegas, go in October. They could also travel North to Utah (best US state for motorcycle travel next to California) or head West over the Sierra Nevada mountains to Yosemite, Sequoia National Parks and onto the Pacific Coast Highway. Our Sierra Nevada is beautiful with great roads in Autumn. (Fall)

14 days is a short time to do exploring. Better to take at least a month and find a cheaper bike to rent. I would try to rent a bike from a private party (if you can find someone willing). Maybe spend half of the $200 per day rate?

Also, a Honda Gold Wing is better for touring Two-Up than a Harley. Contact the big Gold Wing clubs in USA ... see if someone would rent your parents a bike. You never know.