I try to do some exercise every day. When it comes to sports, TO DO is the verb you have to use.

To try to maintain the original meaning of this sentence, I think "I try to exercise alittle every day." reads more naturally <3 But if I heard someone say "I try to do some exercise every day." in conversation, I wouldn't immidiately notice anything was off.

I try to exercise. Period. (The rest is unnecessary in day to day conversation with native speakers in an informal setting.)