Tulips like to be on the dry side in summer, so how about something drought tolerant, like Snow-in-Summer (Cerastrium tomentosum) or hardy iceplants (Delosperma species). People who actually live in a cold climate probably have a lot more suggestions: I'm just harking back to my college days in Flagstaff, AZ (z 5). : )

I'm not sure how hardy any of these would be for you, but here goes: Paeony, Delphinium, Euphorbia (the coloured ones not the 'weeds'!), Salvia, Scabious, Aubrieta, dwarf bearded Iris, Helleborus foetida (more for foliage than flowers once the tulips have gone) 'daisies' - eg Arctotis, Gazania, Osteospermum - Verbena and Verbascum, Origanum, Penstemon, Nicotiana, Dianthus annual and perennial.

Unless you're aiming for a massive 'show' of tulips it might help to make them more like temporary decorations for the main display. Patches of delightful colour while the main show is coming into leaf and bud.

With big displays the 'easiest way' is to lift all the bulbs, feed the ground richly, and plant out your bedding plants to give a further magnificent display. (It helps to have hired help for this kind of production.)