It depends on what kind of cognitive load you are trying to induce and what the theoretical basis is. However, in practical terms a syncopated tapping task can load STM/WM shouldn't interfere with the completion of the primary tasks (if they are verbal responses), e.g. http://www.tandfonline.com/doi/abs/10.1080/09541440902793731

as Edward said, before deciding the kind of task to use you need to define several aspects of this task and it also depends on your conception of the resources available for processing (do you consider an energetic or unitary view such as Cowan, or Ellis & ashbrook) or componential models such as Baddeley's WM?

Additionally, do you want to collect data about the loading task? I recommend collecting performance measures for the loading task as you will be able to analyze whether participants have indeed focused on this task.

Do you want to interfere with processing involved in the sentence completion task? In this case, you need to have a task that also requires similar verbal processes, such a verbal load (with digits?), or in other terms that interfere with processing in the phonological loop.

Finally, you may also consider having two groups with different loads: low and high. However, it is better to collect data about the sentence completion task performed in single task situation. 

I often use secondary tasks in my research on writing (Olive, 2004 for example, or Olive 2010 the section on secondary tasks).

Hope this will help

Thierry

I have asked participants to memorise a 6 digit number before a task and advised them that they would be asked to recall it in X minutes time.  They then completed the task of interest, followed by recalling the number by typing it into a field.  This form of cognitive load successfully revealed latent depression-related cognitive biases. 

Thanks a lot for all these advices. They are so helpful and sorry for this imprecise description of  the whole experiment. Therefore I will give you a better description.

My research project deals with the question whether the working memory has its impact on agreement production.

There are the so-called attraction errors: the exam for the students are difficult. Instead of is the speaker produced are because of the interfering number feature of students.

There are studies which show evidence for an influence of the working memory on agreement production but the results are quite mixed. Furthermore studies dealing with number agreement often used a sentecne completion paradigm, which is probelmatic since it is not a pure production task. My goal is to induce more attraction errors (the apple near the pears are red) because of cognitive load and to show a task effect.

The tasks:

First, participants will see an adjective (difficult) and then a preamble (the exam for the students). They have to keep both in mind to complete the whole sentence with the correct verb form of to be (the exam for the students is difficult).

In the picture description paradigm, subjects will see a picture on the screen (an apple on the left side and two pears on the right) and a colored box indicating red for example. They have to produce: the apple near the pears is red.

There are some studies on S-V agreement that used secondary task with writing the sentence. Check for papers published by Fayol, Largy, or Hupet.

Fayol, M., Hupet, M., & Largy, P. (1999). The acquisition of subject-verb agreement in written French: From novices’ to experts’ errors. Reading and Writing, 11, 153–174.

Fayol, M., Largy, P., & Lemaire, P. (1994). Cognitive overload and orthographic errors. A study in French written language. Quarterly Journal of Experimental Psychology, 47, 437–464.

Hupet, M., Fayol, M., & Schelstraete, M.A. (1998). Effects of semantic variables on the subject-verb agreement processes in writing. British Journal of Psychology, 89, 59–75.

https://link.springer.com/article/10.1023/A%3A1008038127807?no-access=true

However, it is not exactly you were looking for, but would be helpful for those whom still looking for a task to induce cognitive load. We have developed a task through which working memory, verbal perception, eye-hand coordination, and selective attention should be engaged in a concurrent manner. Here you can download the task:

Code WAME1.0, a standardized functional computer task to induce m...

It is the task used in the following studies:

Article Eye movement characteristics reflected fatigue development i...

and

Article Reliability of Oculometrics during a Mentally Demanding Task...

Best,

Ramtin