Praying Obligatory Prayers (in Sickness):

Quran mentions that "Allah desires for you ease; He desires not hardship for you." [Surah Bakarah: 185]

If one is unable to sit (when unsafe if pray standing), then he/she may even pray lying down.

Praying Non-Obligatory Prayers (in Sickness):

One may make non-obligatory prayers (voluntary or Witr) while sitting without an excuse.  However, a parson earns half the reward of perfroming same salah salah while standing.

• He (sallallaahu 'alaihi wa sallam) prayed sitting during the illness of which he died." (15) 
• He also prayed sitting on another occasion before that, when he was injured, and the people behind him prayed standing; so he indicated to them to sit, so they sat (and prayed). When he finished, he said:

”You were going to do as the Persians and the Romans do: stand for their kings who sit. So do not do so, for the Imaam is there to be followed: when he makes rukoo', make rukoo', when he rises, rise; and when he prays sitting, pray sitting [all of you].” (16)

Manners of Praying While Sitting or Lying Down:

When making Salãh while sitting, one should make Ruku by supporting himself on his knees and moving his head forward.  He should make the Sajdah as usual by placiing his head and all the "seven bones" on the ground (see picture making Sajdah on "seven Bones").  If it is too difficult to make sajdah on teh ground, then he may make Sajdah while sitting by leaning his head forward and lowering it slightly more than how he made Ruku in ourder to differentiate teh Sajda from teh Ruku.

Rahman, M. Mushfiqur. Performing Salah Using the Prophetic Example (Color): Based on Authentic Hadiths From the Six Most Authentic Books. P 50, Fitrah, 2015. Print