tiredly

Can I form adverbs from past participles by adding the suffix "-ly"?
Can I say "tiredly" or is it better to express it in a different way? e.g.: "I was very tired when I was reading that book."

Sure you can but if in doubt, check a dictionary.

http://dictionary.cambridge.org/define.asp?key=83355&dict=CALD

With lots of past participles, this won't work at all:

beenly
hadly
gonely
sungly
drivenly
donely
thoughtly
eatenly
pickedly

It should work if & only if the past participle forms an adjective.

<<drivenly
>>

I can see 'drivenly' being used as an adverb:

Being an over-achiever at work, the man drivenly got the packages out on time.

Never heard this word before, but there's nothing to proclude its use in English. We make new uses for words all the time with no difficulty. Use of 'drivenly' doesn't break any rules...

Sounds right to me, also "driven" can be an adjective.

I suppose a good example of this is "repeatedly", which you often see.

<<It should work if & only if the past participle forms an adjective. >>

Isn't "done" an adjective in the following sentence:

I don't think it's a done deal yet.

"donely" doesn't seem to be in common use in English.

Another example: "John is his given name." Givenly seems to be uncommon also.

There's always an exception to every rule ... including this one.