Asking your students flat out "What would motivate you to learn this?" may seem silly or ridiculous, but the fact is, who knows better what will motivate your students than themselves. You will probably get a lot of answers like "A pizza party!" or "Extra recess!" Don't disregard these, but don't make a carrot-on-a-string the centerpiece of your strategy. Ask them specifically what kinds of activities you have done in math, or even in other classes, that they found fun. Make sure to emphasize the "fun" part, which will help get them excited about the activities you will be doing in the future.
Fourth-graders are at an age when they have more energy than they know what to do with, and for some, just being indoors can sap their enthusiasm. Try to plan for at least one outdoor activity involving multiplication facts each week. These can be simple things with no materials but flashcards, or more elaborate ones with chalk, rubber balls, jump ropes --- the sky's the limit. The most important this is that students move around while they are doing the activity. Even more than helping them practice, this will get them to associate math with having fun rather than being bored, which will encourage them become more self-motivated.
One of the key tools of motivation is getting students to understand why a subject is worth learning in a real-life context. Invite parents who use multiplication in their jobs to give a short (five to 10 minute) talk. When you send out invitations to parents, be as open as possible --- many, if not most, vocations involve multiplication of some kind, whether it is an accountant with a ledger book or a cook with eggs and slices of red peppers. The time limit is also an important factor --- the attention span of a fourth grader is quite short, and trying to do a longer talk will probably lead to glazed eyes instead of the motivation you want.
Fourth-graders have very active hands, and often pressing a pencil to a piece of paper just isn't enough. Just like the physical activities, activities that let students use their imagination get them to associate math with fun rather than boredom create a kind of motivation that will persist after the lesson is over. The important thing is to make these crafts both structured and open-ended. For example, have student students draw a comic strip where the main character solves a multiplication problem. Even something as simple as letting students color and decorate their times-table charts can create motivation by giving students ownership of their learning materials.