Ok, I have it working.
Thank you for pointing me in the right direction about the compiler not working well with the 1947 chip yet.

Here is what I did to make it work:
(I only need to send one byte at a time at 2400 baud, so it works ok for now)

Include "modedefs.bas"

ANSELF = 0
TrisF = 0

SO var PortF.2
Pattern var byte

Start:

Pause 200
Pattern = Pattern + 1
Gosub SendSerial ' Serout PortF.2,4,[Pattern]
Goto Start

SendSerial:
High SO
PauseUs 416

If Pattern.0 = 1 then
High SO
PauseUS 410
Else
Low SO
PauseUS 410
Endif

If Pattern.1 = 1 then
High SO
PauseUS 410
Else
Low SO
PauseUS 410
Endif

If Pattern.2 = 1 then
High SO
PauseUS 410
Else
Low SO
PauseUS 410
Endif

If Pattern.3 = 1 then
High SO
PauseUS 410
Else
Low SO
PauseUS 410
Endif

If Pattern.4 = 1 then
High SO
PauseUS 410
Else
Low SO
PauseUS 410
Endif

If Pattern.5 = 1 then
High SO
PauseUS 410
Else
Low SO
PauseUS 410
Endif

If Pattern.6 = 1 then
High SO
PauseUS 410
Else
Low SO
PauseUS 410
Endif

If Pattern.7 = 1 then
High SO
PauseUS 410
Else
Low SO
PauseUS 410
Endif

Low SO
PauseUS 416

Return