Side chains are constrained by a fixed number of coins. As far as I can see, without an emission of new coins there is no practical way to secure them with one notable exception; namely demurrage. The credit for this belongs to Freicoin http://freico.in/

I know this is controversial but it can work, particularly for a side chain whose purpose is transactions as opposed to wealth storage. A 1% per year demurrage rate is not a real issue if the velocity of money is say 2 weeks.