No where in any of the definitions of Trial by Combat does it mention anything regarding punishment.
A trial is to determine guilt or innocence, trial by combat makes "The Gods" the judges, sentencing is a separate process to decide what the punishment is. Presumably "The Gods" are more than capable of doling out punishment if they see fit.
Tyrion is still going to be sentenced by humans and human law that states the sentence for regicide is death, "The Gods" have nothing to do with that. But human law also includes the caveat that a person can join the Night's Watch to be abolished of all crimes, by promising to serve in protection of the realm and giving up everything they once held.
If someone can take the Black after being found guilty of regicide is the legal question and, in the AGOT lore, I don't believe there is any precedent either way.
Could "The Crown" (Tywin) allow Tyrion to take the black? Yes.
Will "The Crown" allow Tyrion to take the black? Who knows?