I haven't. I had a look online and found this study...
"In conclusion, although the bioavailability of LT4 is lower after administration of the suppository than after the oral formulation, it was suggested that T4 levels can be maintained in patients with hypothyroidism by administering LT4 suppositories at a dose 1.8 times higher than that of the tablet. Thus, the administration of LT4 suppository can be an alternative for treatment with oral medication in clinical practice."
Clinical efficacy and pharmacokinetics of levothyroxine suppository in patients with hypothyroidism.
Kashiwagura Y, et al. Biol Pharm Bull. 2014;37(4):666-70.
It's not usually the levothyroxine (the active ingredient in replacement thyroid hormone medications) that causes people to have trouble taking them. Typically, the problem is fillers, binders or dyes. There are a number of manufacturers of Levothyroxine and each one uses different ingredients, except for the levo, itself. For instance, Synthroid uses acacia and corn starch, either of which bothers many people... I didn't do well on Synthroid, but I do well on Levoxyl. Others do best on Tirosint, which is a gelcap and contains only the levothryoxine, gelatin, water and glycerin. Tirosint works very well and I took it for several years due to absorption issues, but it became too expensive and I couldn't justify the cost so I switched to Levoxyl on which I do quite well. They do have programs through which some people can get it free of cost or at reduced rates.
You can check your prescription bottle for the manufacturer of your particular medication and find out the ingredients, if you want to determine why it might be hard on your digestive system. Alternatively, you could simply have your compounding pharmacy make capsules using a filler you know doesn't bother you.