OK here's my attempt. To be long Theta you need to have an overall short strategy and you want the position to go down in price. Any increase in volatility will make the option's value increase. Therefore, I don't think it's possible to be long both Theta and Vega at the same time.
It might be possible in some kind of skew position. For example if you are short call skew. But you aren't really long vol and you aren't really receiving theta.
Here are quite a few long theta long vega trades: http://www.homeoptionstrading.com/_Media/home-options-trading-define-2.png
ATM flies are long theta in most cases and neutral to short a few $ in vega. You're not going to get any closer (at inception) to +theta+vega.
In the spooz, you can concoct a collar that would be long vega and long theta. Of course, it would not be long vega when you need it
A Reverse Butterfly, as long as you start off outside any of the short strikes. Dont get get sucked into the hole. :eek: Maybe not what you are looking for.