I am looking for trees with a noninvasive root system to put near pavers?

Trees all have root systems that are invasive to a degree: some are worse than others. notoriously bad are cherry and willow - both have roots taht are quite close to surface and that increase in girth causing heave. Choose small varieties that have smaller systems, avoid cherry, willow, poplar, alder and other high-water take-up trees, choose drought-tolerant varieties. Another option is to lay your paving to accommodate tree roots - use a root barrier, or use a base layer of Amsterdam soil or other granualar material that will be less affected by roots. If the paving is impervious, roots will not favour growing below them anyway, unless is it a narrow area that roots can grow underneath to reach a favourable rooting area the other side.