The Chazon Ish zt”l once advised a student who had a hard time studying Torah for long periods of time to just learn a little bit from many different sefarim, because many short tasks are more manageable than one large task. 

For example, studying 10 minutes of chumash, 10 minutes of Nach, then halacha, gemara, Mishna and mussar will add up to an hour, yet without the pressure and heaviness of a long chore. 

This can be applied to tefillah as well.  Instead of putting pressure on yourself to daven with kavanah for the entire davening, start with breaking it down into sections which is more manageable.  Then work on the next section of tefillah.