There are some other words but not many, it can depend on the situation you are encouraging someone with.
You can say I supported Ann while she was going through a difficult time.
I supported her to write her English homework. This last sentence is correct but it is not quite the same as encourage :)
You could use cheer if it is a race, I cheered her on during the race, which is similar to I encouraged her on during the race.
You could use helped as it has more uses, I helped her to study, I helped her during her difficult time. I helped them when they were feeling sad. This is similar to encourage.