We've done Eye of Round low & slow with some great results.
Coat with some yellow, or better yet, brown mustard and whatever seasoning you like (you do not need oil for this method). Stick a probe in the center to monitor the Internal Temperature, and roast in your smoker relatively low & slow, around 250° - 275°, until it reaches about 120° - 130° I.T. (depending on whether you like it more rare, or mid-rare). Do NOT go beyond 130°
Lastly, and this is crucial, for tender eye of round you MUST allow it to rest, tented with foil (not wrapped), for a MINIMUM 30 - 45 MINUTES!!! It will continue to rise in temperature about 8° or so during the rest. When the Internal Temp levels out and starts to drop, THAT'S when you know it's ready to slice.
I mean it; Do NOT cook it beyond 130°, and for 30 - 45 minutes do NOT cut into it, don't touch it, don't even look at it! You will be rewarded with a surprisingly fairly tender, juicy and flavorful cut of inexpensive meat.