Before checking this hadith I first want to point at the fact that this dua' comes from the Quran (9:129):
But if they turn away, [O Muhammad], say, "Sufficient for me is Allah; there is no deity except Him. On Him I have relied, and He is the Lord of the Great Throne."
therefore it is absolutely allowed to use it in your supplication.
What needs to be checked are the following points: Is there any authentic hadith giving a hint about the amount of repeats or a special time to say this dua'?
You'll find this hadith in sunan abi Dawod where it is a mawqouf hadith this means it is a kind of saying of a sahabi (in this case abu Darda'), but as the content (time and amount of repetitions) isn't of the kind which can be based on ijtihad or any kind of opinion it should be regarded as a marfo' hadith (abu Darda' said what our Prophet has said). Ibn Kathir in his commentary of verse 9:129 considered the statement or addition
... "whether he is true or false in (repeating) them."
as gharib (strange) and qualified it as monkar (rejected).
Al-Albani qualified the whole hadith as fabricated (I'd like to know why?).
Shoa'ib and Abdulqadir al-Arnaout qualified the sanad (narrator chain) of abi Dawod as sahih as you may read in this fatwa.
Ibn Bazz qualified it as da'if (see here).
Ibn as-Sunni has compiled a similar narration with a complete sanad, but the strongest version -according scholars- is the mawquf version. Both versions are also compiled in ibn 'Asakirs "tareekh Dimashq" (see also).
A similar statement is also in "Ad-du'a" by at-Tabarni:
من قال: حسبي الله، لا إله إلا هو، عليه توكلت، وهو رب العرش العظيم؛ قال الله: لأكفين عبدي صادقًا كان أو كاذبًا
If anyone says seven times morning and evening; “Allah sufficeth me: there is no god but He; on him is my trust- he, the Lord of the Throne (of glory) Supreme”, Allah said: "I will be sufficient for my slave against anything which grieves him, whether he is true or false in (saying) them."
(Source: ahlalhadeeth (archive) or alukah where most of the above content also was discussed)
So on the whole the supplication itself is part of the Quran and therefore absolutely valid, the addition "whether he is true or false in (repeating) them." is the strongest reason for considering it a weak, fabricated or rejected hadith. While the rest of the hadith could be acceptable! (See also
Some authentic du'a for fulfillment of wishes
This is basically taken from this fatwa in Arabic:
"There is no deity except You; exalted are You. Indeed, I have been of the wrongdoers."
- If you asked Allah by his greatest name (see in Sunan ibn Majah).
- The prayer of need as stated in Jami' at-Tirmidhi.
Note that you should also choose a good time to do your supplication etc.
See also this article on IslamOnline and this fatwa on islamWay.