Interest rates in a deflationary currency

[NewLiberty]

If you have a deflationary currency I am at a loss to why you would need to pay interest on a loan?

A rational market wouldn't.

This changes in times of inflation (economic activity starts to shrink low supply and high demand) then the rational market would be willing to pay interest and borrow with interest.  
Until then, save your cryptos,

Default risk provides a reason for interest on a loan even in a preemptively deflationary currency.

[NewLiberty]

I was under the impression inflation is caused by an increase in the money supply (Quantitative easing for example) and as the creation of money is controlled at a sustained rate by the Bitcoin network and has a set upper limit - there should be no inflation?

This doesn't seem to follow: "bitcoin/fiat has (controlled) inflation => there should be no inflation"

Maybe if you discern "money supply inflation" and "price inflation" you'll get a clearer picture.

If bitcoin was the only money used in a certain growing economy (at a higher than the current bitcoin money supply inflation rate) prices would generally fall.

Yes.
Money supply and inflation are linked but it is not a perfect link, there are other factors, namely demand (for both the money and for the goods).
If there is a scarcity in a particular good, its price will rise against the currency.  For example in a disaster, there may be a great deal of things which are scarce and so there can be external reasons for inflation, not just the rate of money creation.
You've heard the saying "save for a rainy day"?  Its never quoted corollary is "spend on rainy days".

[painlord2k]

There is no incentive to loan money in a deflationary currency where the economy is growing.  Why risk not being repaid when the potential lender can just sit on his or her pile of bitcoins and see their value rise (buy more goods per bitcoin) without lifting a single finger?

Wrong.
There is no incentive to loan money if the interest rate paid is not high enough.

If the interest rate is 10%/year and the return of keeping the money is 3% increase of purchasing power without risks, someone will loan money at 10% rate, if they had enough money to loan and take risks (if they are able to save). They will accept the risks and will take the gains a year later.

As saving increase the capital available, the utility of saving will reduce.
Then, instead of saving, people will start to loan.
First loans to be done will be the loans able to generate an higher rate of return.
If there is more capital available, other loans with a lower rate of return will be made.

[User705]

Until we manage to become immortal there will always be interest which is time preference, because things (money, goods, assets, btc) will always be worth more to you the day before you die then the day after.  Everything else is just the market that seeks equilibrium and until we become all knowing gods each one of us will have an imperfect view of such markets and we will therefore be able to make deals with each other because of differing veiws on time preferences.  Also notice how those who cry out that interest is evil usury want to replace the market with a system that benefits them personally even if indirectly much like government operators who draw enourmous salaries and benefits for administering such a system all the while claiming its for all of our benefit.  Therefore it doesn't matter if a currency is deflationary, inflationary or sea shells there will always be interest.